Add backend API checks on CI #4817

Job	Run time
pre-commit / pre-commit	2m 39s
pre-commit / link-check	16s
ubuntu / gcc-build (ubuntu-24.04, Debug)	2m 11s
ubuntu / gcc-build (ubuntu-24.04, Release)	2m 30s
mac / clang-build (Release)	3m 46s
windows / msvc-build (Debug)	2m 53s
ubuntu / clang-build (ubuntu-24.04)	2m 41s
windows / clang-build	3m 43s
windows / msvc-build (Release)	4m 45s
mac / clang-build (Debug)	2m 25s
mac / clang-test	4m 20s
windows / clang-test	4m 55s
windows / msvc-test	5m 3s
ubuntu / gcc-test (ubuntu-24.04)	8m 33s
ubuntu / clang-test (ubuntu-24.04)	8m 53s
ubuntu / clang-sanitizer-build (ubuntu-24.04)	3m 21s
mac / clang-test-extended	3m 1s
ubuntu / gcc-test-extended (ubuntu-24.04)	4m 49s
windows / clang-test-extended	2m 55s
windows / msvc-test-extended	3m 49s
ubuntu / clang-sanitizer-test (ubuntu-24.04)	2m 54s
ubuntu / clang-test-extended (ubuntu-24.04)	4m 44s
ubuntu / clang-sanitizer-test-extended (ubuntu-24.04)	2m 42s
ubuntu / gcc-build-codecov	7m 23s
perf / ubuntu-gcc-build-perf-stats	1m 26s
perf / macos-clang-build-perf-stats	1m 46s
pages / build-scoreboard	15s
pages / build-doxygen-xml	22s
pages / build-sphinx	39s
pages / deploy-pages	0s
	1h 39m 39s

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