diff --git a/pyproject.toml b/pyproject.toml
index d8b554388..a345fe34d 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -34,13 +34,13 @@ test = [
     "argcomplete>=3.0.3; python_version < '3.12'",
     "argcomplete>=3.5.2; python_version >= '3.12'",
     # See https://github.com/python/mypy/issues/20329 for PyPy support issue.
-    # Also, test assertions will need to be updated for 1.20+ because
-    # `reveal_type()` representations were simplified in
-    # https://github.com/python/mypy/pull/20929
-    "mypy>=1.17.0,<1.19",
+    # `reveal_type()` representations were simplified (dropping the `builtins.`
+    # prefix) in https://github.com/python/mypy/pull/20929; test assertions in
+    # tests/test_typing.py target that newer output, so require >=1.20.
+    "mypy>=1.20; implementation_name != 'pypy'",
     "pre-commit",
     "pytest-mock",
-    "pytest-mypy-testing",
+    "pytest-mypy-testing; implementation_name != 'pypy'",
     "pytest>=7.0,<10.0",
 ]
 docs = [
@@ -98,6 +98,14 @@ show_error_context = true
 warn_unreachable = true
 exclude = ["examples/docs/configs", "traitlets/tests/test_typing.py"]
 
+[[tool.mypy.overrides]]
+# numpy is pulled in transitively via `import pytest` (pytest.approx). Its
+# recent stubs use the `type` statement, which mypy rejects under
+# python_version = "3.10", aborting the check. Skip following into it.
+module = "numpy.*"
+follow_imports = "skip"
+follow_imports_for_stubs = true
+
 [tool.pytest.ini_options]
 minversion = "6.0"
 xfail_strict = true
diff --git a/tests/conftest.py b/tests/conftest.py
new file mode 100644
index 000000000..d8017da6b
--- /dev/null
+++ b/tests/conftest.py
@@ -0,0 +1,11 @@
+from __future__ import annotations
+
+import sys
+
+collect_ignore = []
+
+# mypy does not support PyPy (https://github.com/python/mypy/issues/20329), so
+# neither mypy nor pytest-mypy-testing is installed there and the mypy_*_typing
+# checks cannot run.
+if sys.implementation.name == "pypy":
+    collect_ignore.append("test_typing.py")
diff --git a/tests/test_typing.py b/tests/test_typing.py
index 308ea21f1..44b3a32e6 100644
--- a/tests/test_typing.py
+++ b/tests/test_typing.py
@@ -59,7 +59,7 @@ def _foo_validate(self, commit: t.Any) -> bool:
             return True
 
     t = T()
-    reveal_type(t.foo)  # R: builtins.str
+    reveal_type(t.foo)  # R: str
     reveal_type(t._foo_observer)  # R: Any
     reveal_type(t._foo_validate)  # R: Any
 
@@ -100,14 +100,14 @@ class T(HasTraits):
         ).tag(config=True)
 
     t = T()
-    reveal_type(List(["foo"]))  # R: traitlets.traitlets.List[builtins.str]
-    reveal_type(List([""]).tag(sync=True))  # R: traitlets.traitlets.List[builtins.str]
+    reveal_type(List(["foo"]))  # R: traitlets.traitlets.List[str]
+    reveal_type(List([""]).tag(sync=True))  # R: traitlets.traitlets.List[str]
     reveal_type(List(None, allow_none=True))  # R: traitlets.traitlets.List[Never]
     reveal_type(
         List(None, allow_none=True).tag(sync=True)  # R: traitlets.traitlets.List[Never]
     )
-    reveal_type(T.latex_command)  # R: traitlets.traitlets.List[builtins.str]
-    reveal_type(t.latex_command)  # R: builtins.list[builtins.str]
+    reveal_type(T.latex_command)  # R: traitlets.traitlets.List[str]
+    reveal_type(t.latex_command)  # R: list[str]
 
 
 @pytest.mark.mypy_testing
@@ -116,12 +116,12 @@ class T(HasTraits):
         foo = Dict({}, help="Shell command used to compile latex.").tag(config=True)
 
     t = T()
-    reveal_type(Dict(None, allow_none=True))  # R: traitlets.traitlets.Dict[builtins.str, Any]
+    reveal_type(Dict(None, allow_none=True))  # R: traitlets.traitlets.Dict[str, Any]
     reveal_type(
-        Dict(None, allow_none=True).tag(sync=True)  # R: traitlets.traitlets.Dict[builtins.str, Any]
+        Dict(None, allow_none=True).tag(sync=True)  # R: traitlets.traitlets.Dict[str, Any]
     )
-    reveal_type(T.foo)  # R: traitlets.traitlets.Dict[builtins.str, Any]
-    reveal_type(t.foo)  # R: builtins.dict[builtins.str, Any]
+    reveal_type(T.foo)  # R: traitlets.traitlets.Dict[str, Any]
+    reveal_type(t.foo)  # R: dict[str, Any]
 
 
 @pytest.mark.mypy_testing
@@ -162,8 +162,8 @@ class KernelSpecManager(HasTraits):
     t = KernelSpecManager()
     reveal_type(t.kernel_spec_class)  # R: def () -> tests.test_typing.KernelSpec@129
     reveal_type(t.kernel_spec_class())  # R: tests.test_typing.KernelSpec@129
-    reveal_type(t.kernel_spec_class().item)  # R: builtins.str
-    reveal_type(t.other_class)  # R: builtins.type
+    reveal_type(t.kernel_spec_class().item)  # R: str
+    reveal_type(t.other_class)  # R: type
     reveal_type(t.other_class())  # R: Any
     reveal_type(t.other_kernel_spec_class)  # R: def () -> tests.test_typing.KernelSpec@129
     reveal_type(t.other_kernel_spec_class())  # R: tests.test_typing.KernelSpec@129
@@ -185,29 +185,29 @@ class T(HasTraits):
 
     t = T()
     reveal_type(
-        Unicode(  # R: traitlets.traitlets.Unicode[builtins.str, builtins.str | builtins.bytes]
+        Unicode(  # R: traitlets.traitlets.Unicode[str, str | bytes]
             "foo"
         )
     )
     reveal_type(
-        Unicode(  # R: traitlets.traitlets.Unicode[builtins.str, builtins.str | builtins.bytes]
+        Unicode(  # R: traitlets.traitlets.Unicode[str, str | bytes]
             ""
         ).tag(sync=True)
     )
     reveal_type(
-        Unicode(  # R: traitlets.traitlets.Unicode[builtins.str | None, builtins.str | builtins.bytes | None]
+        Unicode(  # R: traitlets.traitlets.Unicode[str | None, str | bytes | None]
             None, allow_none=True
         )
     )
     reveal_type(
-        Unicode(  # R: traitlets.traitlets.Unicode[builtins.str | None, builtins.str | builtins.bytes | None]
+        Unicode(  # R: traitlets.traitlets.Unicode[str | None, str | bytes | None]
             None, allow_none=True
         ).tag(sync=True)
     )
     reveal_type(
-        T.export_format  # R: traitlets.traitlets.Unicode[builtins.str, builtins.str | builtins.bytes]
+        T.export_format  # R: traitlets.traitlets.Unicode[str, str | bytes]
     )
-    reveal_type(t.export_format)  # R: builtins.str
+    reveal_type(t.export_format)  # R: str
 
 
 @pytest.mark.mypy_testing
@@ -221,12 +221,12 @@ class T(HasTraits):
 
     t = T()
     reveal_type(
-        Enum(  # R: traitlets.traitlets.Enum[builtins.str]
+        Enum(  # R: traitlets.traitlets.Enum[str]
             ("foo",)
         )
     )
     reveal_type(
-        Enum(  # R: traitlets.traitlets.Enum[builtins.str]
+        Enum(  # R: traitlets.traitlets.Enum[str]
             [""]
         ).tag(sync=True)
     )
@@ -241,9 +241,9 @@ class T(HasTraits):
         ).tag(sync=True)
     )
     reveal_type(
-        T.log_level  # R: traitlets.traitlets.Enum[builtins.int]
+        T.log_level  # R: traitlets.traitlets.Enum[int]
     )
-    reveal_type(t.log_level)  # R: builtins.int
+    reveal_type(t.log_level)  # R: int
 
 
 @pytest.mark.mypy_testing
@@ -277,9 +277,9 @@ class T(HasTraits):
     reveal_type(Set(None, allow_none=True))  # R: traitlets.traitlets.Set
     reveal_type(Set(None, allow_none=True).tag(sync=True))  # R: traitlets.traitlets.Set
     reveal_type(T.remove_cell_tags)  # R: traitlets.traitlets.Set
-    reveal_type(t.remove_cell_tags)  # R: builtins.set[Any]
+    reveal_type(t.remove_cell_tags)  # R: set[Any]
     reveal_type(T.safe_output_keys)  # R: traitlets.traitlets.Set
-    reveal_type(t.safe_output_keys)  # R: builtins.set[Any]
+    reveal_type(t.safe_output_keys)  # R: set[Any]
 
 
 @pytest.mark.mypy_testing
@@ -312,33 +312,33 @@ class T(HasTraits):
 
     t = T()
     reveal_type(
-        Bool(True)  # R: traitlets.traitlets.Bool[builtins.bool, builtins.bool | builtins.int]
+        Bool(True)  # R: traitlets.traitlets.Bool[bool, bool | int]
     )
     reveal_type(
-        Bool(  # R: traitlets.traitlets.Bool[builtins.bool, builtins.bool | builtins.int]
+        Bool(  # R: traitlets.traitlets.Bool[bool, bool | int]
             True
         ).tag(sync=True)
     )
     reveal_type(
-        Bool(  # R: traitlets.traitlets.Bool[builtins.bool | None, builtins.bool | builtins.int | None]
+        Bool(  # R: traitlets.traitlets.Bool[bool | None, bool | int | None]
             None, allow_none=True
         )
     )
     reveal_type(
-        Bool(  # R: traitlets.traitlets.Bool[builtins.bool | None, builtins.bool | builtins.int | None]
+        Bool(  # R: traitlets.traitlets.Bool[bool | None, bool | int | None]
             None, allow_none=True
         ).tag(sync=True)
     )
     reveal_type(
-        T.b  # R: traitlets.traitlets.Bool[builtins.bool, builtins.bool | builtins.int]
+        T.b  # R: traitlets.traitlets.Bool[bool, bool | int]
     )
-    reveal_type(t.b)  # R: builtins.bool
-    reveal_type(t.ob)  # R: builtins.bool | None
+    reveal_type(t.b)  # R: bool
+    reveal_type(t.ob)  # R: bool | None
     reveal_type(
-        T.b  # R: traitlets.traitlets.Bool[builtins.bool, builtins.bool | builtins.int]
+        T.b  # R: traitlets.traitlets.Bool[bool, bool | int]
     )
     reveal_type(
-        T.ob  # R: traitlets.traitlets.Bool[builtins.bool | None, builtins.bool | builtins.int | None]
+        T.ob  # R: traitlets.traitlets.Bool[bool | None, bool | int | None]
     )
     # we would expect this to be bool | int | None, but...
     t.b = "foo"  # E: Incompatible types in assignment (expression has type "str", variable has type "bool | int")  [assignment]
@@ -352,24 +352,24 @@ class T(HasTraits):
         oi: Int[int | None, int | None] = Int(42, allow_none=True).tag(sync=True)
 
     t = T()
-    reveal_type(Int(True))  # R: traitlets.traitlets.Int[builtins.int, builtins.int]
-    reveal_type(Int(True).tag(sync=True))  # R: traitlets.traitlets.Int[builtins.int, builtins.int]
+    reveal_type(Int(True))  # R: traitlets.traitlets.Int[int, int]
+    reveal_type(Int(True).tag(sync=True))  # R: traitlets.traitlets.Int[int, int]
     reveal_type(
-        Int(  # R: traitlets.traitlets.Int[builtins.int | None, builtins.int | None]
+        Int(  # R: traitlets.traitlets.Int[int | None, int | None]
             None, allow_none=True
         )
     )
     reveal_type(
-        Int(  # R: traitlets.traitlets.Int[builtins.int | None, builtins.int | None]
+        Int(  # R: traitlets.traitlets.Int[int | None, int | None]
             None, allow_none=True
         ).tag(sync=True)
     )
-    reveal_type(T.i)  # R: traitlets.traitlets.Int[builtins.int, builtins.int]
-    reveal_type(t.i)  # R: builtins.int
-    reveal_type(t.oi)  # R: builtins.int | None
-    reveal_type(T.i)  # R: traitlets.traitlets.Int[builtins.int, builtins.int]
+    reveal_type(T.i)  # R: traitlets.traitlets.Int[int, int]
+    reveal_type(t.i)  # R: int
+    reveal_type(t.oi)  # R: int | None
+    reveal_type(T.i)  # R: traitlets.traitlets.Int[int, int]
     reveal_type(
-        T.oi  # R: traitlets.traitlets.Int[builtins.int | None, builtins.int | None]
+        T.oi  # R: traitlets.traitlets.Int[int | None, int | None]
     )
     t.i = "foo"  # E: Incompatible types in assignment (expression has type "str", variable has type "int")  [assignment]
     t.i = None  # E: Incompatible types in assignment (expression has type "None", variable has type "int")  [assignment]
@@ -383,21 +383,21 @@ class T(HasTraits):
         oi = CInt(42, allow_none=True).tag(sync=True)
 
     t = T()
-    reveal_type(CInt(42))  # R: traitlets.traitlets.CInt[builtins.int, Any]
-    reveal_type(CInt(42).tag(sync=True))  # R: traitlets.traitlets.CInt[builtins.int, Any]
+    reveal_type(CInt(42))  # R: traitlets.traitlets.CInt[int, Any]
+    reveal_type(CInt(42).tag(sync=True))  # R: traitlets.traitlets.CInt[int, Any]
     reveal_type(
-        CInt(None, allow_none=True)  # R: traitlets.traitlets.CInt[builtins.int | None, Any]
+        CInt(None, allow_none=True)  # R: traitlets.traitlets.CInt[int | None, Any]
     )
     reveal_type(
-        CInt(  # R: traitlets.traitlets.CInt[builtins.int | None, Any]
+        CInt(  # R: traitlets.traitlets.CInt[int | None, Any]
             None, allow_none=True
         ).tag(sync=True)
     )
-    reveal_type(T.i)  # R: traitlets.traitlets.CInt[builtins.int, Any]
-    reveal_type(t.i)  # R: builtins.int
-    reveal_type(t.oi)  # R: builtins.int | None
-    reveal_type(T.i)  # R: traitlets.traitlets.CInt[builtins.int, Any]
-    reveal_type(T.oi)  # R: traitlets.traitlets.CInt[builtins.int | None, Any]
+    reveal_type(T.i)  # R: traitlets.traitlets.CInt[int, Any]
+    reveal_type(t.i)  # R: int
+    reveal_type(t.oi)  # R: int | None
+    reveal_type(T.i)  # R: traitlets.traitlets.CInt[int, Any]
+    reveal_type(T.oi)  # R: traitlets.traitlets.CInt[int | None, Any]
 
 
 @pytest.mark.mypy_testing
@@ -407,21 +407,21 @@ class T(HasTraits):
         otcp = TCPAddress(None, allow_none=True)
 
     t = T()
-    reveal_type(t.tcp)  # R: tuple[builtins.str, builtins.int]
+    reveal_type(t.tcp)  # R: tuple[str, int]
     reveal_type(
-        T.tcp  # R: traitlets.traitlets.TCPAddress[tuple[builtins.str, builtins.int], tuple[builtins.str, builtins.int]]
+        T.tcp  # R: traitlets.traitlets.TCPAddress[tuple[str, int], tuple[str, int]]
     )
     reveal_type(
-        T.tcp.tag(  # R:traitlets.traitlets.TCPAddress[tuple[builtins.str, builtins.int], tuple[builtins.str, builtins.int]]
+        T.tcp.tag(  # R:traitlets.traitlets.TCPAddress[tuple[str, int], tuple[str, int]]
             sync=True
         )
     )
-    reveal_type(t.otcp)  # R: tuple[builtins.str, builtins.int] | None
+    reveal_type(t.otcp)  # R: tuple[str, int] | None
     reveal_type(
-        T.otcp  # R: traitlets.traitlets.TCPAddress[tuple[builtins.str, builtins.int] | None, tuple[builtins.str, builtins.int] | None]
+        T.otcp  # R: traitlets.traitlets.TCPAddress[tuple[str, int] | None, tuple[str, int] | None]
     )
     reveal_type(
-        T.otcp.tag(  # R: traitlets.traitlets.TCPAddress[tuple[builtins.str, builtins.int] | None, tuple[builtins.str, builtins.int] | None]
+        T.otcp.tag(  # R: traitlets.traitlets.TCPAddress[tuple[str, int] | None, tuple[str, int] | None]
             sync=True
         )
     )