Add Braintrust integration example #1070

Job	Run time
build-lint-test (3.10, macos-arm)	14s
build-lint-test (3.10, windows-latest)	15s
build-lint-test (3.14, macos-intel)	15s
build-lint-test (3.10, ubuntu-latest)	12s
build-lint-test (3.10, macos-intel)	16s
build-lint-test (3.14, ubuntu-latest)	27s
build-lint-test (3.14, windows-latest)	15s
build-lint-test (3.14, macos-arm)	27s
	2m 21s

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