[CI] Integrate lychee action for links availability checks (#742) #4599

Job	Run time
pre-commit / check-file-sizes	3s
pre-commit / link-check	27s
pre-commit / pre-commit	1m 50s
windows / clang-build	2m 11s
mac / clang-build (Debug)	1m 57s
windows / msvc-build (Release)	2m 29s
mac / clang-build (Release)	2m 26s
ubuntu / clang-build (ubuntu-24.04)	2m 58s
ubuntu / gcc-build (ubuntu-24.04, Debug)	2m 4s
ubuntu / gcc-build (ubuntu-24.04, Release)	2m 19s
windows / msvc-build (Debug)	3m 7s
windows / clang-test	2m 51s
ubuntu / gcc-test (ubuntu-24.04)	8m 26s
mac / clang-test	4m 15s
ubuntu / clang-test (ubuntu-24.04)	8m 24s
ubuntu / clang-sanitizer-build (ubuntu-24.04)	3m 10s
windows / msvc-test	4m 44s
windows / clang-test-extended	2m 49s
ubuntu / clang-sanitizer-test (ubuntu-24.04)	2m 53s
mac / clang-test-extended	2m 38s
windows / msvc-test-extended	2m 51s
ubuntu / clang-sanitizer-test-extended (ubuntu-24.04)	2m 41s
ubuntu / gcc-test-extended (ubuntu-24.04)	4m 32s
ubuntu / clang-test-extended (ubuntu-24.04)	4m 34s
ubuntu / gcc-build-codecov	7m 31s
perf / macos-clang-build-perf-stats	1m 57s
perf / ubuntu-gcc-build-perf-stats	1m 26s
pages / build-doxygen-xml	20s
pages / build-scoreboard	18s
pages / build-sphinx	41s
pages / deploy-pages	12s
	1h 29m 4s

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