Add LiteLLM activity sample (#343) #1365

Job	Run time
build-lint-test (3.10, macos-intel)	10m 50s
build-lint-test (3.14, ubuntu-latest)	7m 17s
build-lint-test (3.14, macos-arm)	8m 1s
build-lint-test (3.10, windows-latest)	8m 3s
build-lint-test (3.10, ubuntu-latest)	6m 47s
build-lint-test (3.14, windows-latest)	8m 15s
build-lint-test (3.10, macos-arm)	10m 10s
build-lint-test (3.14, macos-intel)	9m 32s
	1h 8m 55s

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