fix(adk): fix llm span metadata (provider, tools, errors) (#580)

## Summary

Brings the Google ADK integration in line with
`.agents/skills/sdk-integrations/SKILL.md` and cuts the test suite over
to real VCR-backed coverage.

### Integration behavior (`tracing.py`)
- **`metadata.provider="google"` and `metadata.tools` on every `llm`
span.** Tool definitions are lifted out of `input.config` into
`metadata.tools`, preserving Google-native shape.
- **`_capture_config` is now a strict allowlist** — no more
`dict(config)` pass-through. Fields outside the allowlist (including
`tools`/`tool_config`) are dropped from `input.config` automatically.
`_extract_tool_metadata` is the single source of truth for what goes
into `metadata.tools`.
- **`error=e` instead of `error=str(e)`** in the tool and MCP-tool
wrappers — the `Exception` instance flows through to the log pipeline.
- **Trim raw ADK objects from span metadata.** `invocation_context`,
`model_response_event`, `parent_context`, and the `**kwargs` spread
across every wrapper are dropped; only small named fields (`app_name`,
`user_id`, `session_id`, `state_delta`, `agent_name`, `flow_class`,
`tool_class`, `model`, `provider`, `tools`) remain.
- **Drop `_get_field` and `bt_safe_deep_copy(tools)`.** Production ADK
always passes Pydantic objects, so plain `getattr(x, field, default)` is
enough. The log pipeline serializes Pydantic tool objects at send time
(SKILL: "do not over-serialize").

### Tests
- **`test_adk_braintrust_integration`** now filters spans by
`context.span_origin.instrumentation.name == "adk-auto"`, asserts
`{task, llm, tool}` types are covered, and validates
`metadata.provider`, `metadata.tools`, and no tool leakage into
`input.config`.
- **`test_adk_captures_metrics`** asserts `metadata.provider="google"`
and the `direct_response` call-type span name.
- **`test_adk_max_tokens_captures_content`** now also asserts the
sampling config (`max_output_tokens`, `temperature`) is captured in the
LLM span input.
- **`test_adk_sync_runner_run_does_not_duplicate_invocation_spans`** now
also asserts thread-bridge context propagation — every `adk-auto` span
shares the outer parent's `root_span_id`.
- **Delete `test_adk_mcp_tool.py` entirely** (the two remaining
patcher-wiring tests were duplicative of the auto-instrument subprocess
test) and drop its line from `noxfile.py`.
- **Delete fake-LLM, mock, and non-ADK unit tests** — 15 tests removed.
Every branch they covered (`_determine_llm_call_type`, `_capture_config`
allowlist, `_serialize_content/_serialize_part`,
`_serialize_pydantic_schema`, `bt_safe_deep_copy`, sampling config,
thread bridge, PDF attachment, MCP-in-flow parenting, async context) is
exercised by an existing VCR test.

Final test count: **13 tests**, 12 VCR-backed + one plain-Python
regression for the `_create_thread_wrapper` double-invoke bug.

## Test plan

- [x] `nox -s "test_google_adk(latest)"` — 13 passed
- [x] `nox -s "test_google_adk(1.14.1)"` — 13 passed
- [x] No cassettes re-recorded (one orphaned cassette,
`test_adk_agent_metadata_with_attachment.yaml`, removed on both matrix
versions)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

<!-- sfk:created-approved-by -->
Created by abhijeet

<!-- sfk:slack-thread -->
[Slack
thread](https://starfolkai.slack.com/archives/C0AQDETAVT3/p1784214360713409?thread_ts=1784214360.713409&cid=C0AQDETAVT3)

---------

Co-authored-by: Starfolk <noreply@starfolk.ai>
Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>

Author: 3 people

py/noxfile.py

@@ -442,6 +442,11 @@ def test_pydantic_ai_wrap_openai(session, version):
     """Test pydantic_ai with wrap_openai() approach - supports older versions."""
     _install_test_deps(session)
     _install_matrix_dep(session, "pydantic-ai-wrap-openai", version)
+    # pydantic-ai 0.1.9 unconditionally imports ``from opentelemetry._events import Event``.
+    # The ``_events`` module was removed from ``opentelemetry-api`` in 1.40+, so a fresh
+    # resolution on newer opentelemetry releases picks a version that breaks import.
+    if version == "0.1.9":
+        session.install("opentelemetry-api<1.40", silent=SILENT_INSTALLS)
     _run_tests(session, f"{INTEGRATION_DIR}/pydantic_ai/test_pydantic_ai_wrap_openai.py", version=version)
 
 
@@ -513,7 +518,6 @@ def test_google_adk(session, version):
     _install_test_deps(session)
     _install_matrix_dep(session, "google-adk", version)
     _run_tests(session, f"{INTEGRATION_DIR}/adk/test_adk.py", version=version)
-    _run_tests(session, f"{INTEGRATION_DIR}/adk/test_adk_mcp_tool.py", version=version)
 
 
 LANGCHAIN_VERSIONS = _get_matrix_versions("langchain-core")