Add LiteLLM activity sample #1360

Job	Run time
build-lint-test (3.10, windows-latest)	8m 15s
build-lint-test (3.14, macos-arm)	6m 58s
build-lint-test (3.10, ubuntu-latest)	7m 3s
build-lint-test (3.14, macos-intel)	11m 33s
build-lint-test (3.10, macos-intel)	12m 42s
build-lint-test (3.14, windows-latest)	8m 21s
build-lint-test (3.14, ubuntu-latest)	6m 56s
build-lint-test (3.10, macos-arm)	9m 29s
	1h 11m 17s

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