[CI] Integrate lychee action for links availability checks #4588

Job	Run time
pre-commit / check-file-sizes	6s
pre-commit / link-check	20s
pre-commit / pre-commit	2m 13s
mac / clang-build (Debug)	1m 56s
windows / clang-build	2m 2s
ubuntu / gcc-build (ubuntu-24.04, Release)	2m 16s
mac / clang-build (Release)	1m 42s
ubuntu / clang-build (ubuntu-24.04)	2m 44s
windows / msvc-build (Release)	1m 56s
windows / msvc-build (Debug)	3m 3s
ubuntu / gcc-build (ubuntu-24.04, Debug)	1m 59s
mac / clang-test	4m 18s
windows / clang-test	2m 48s
ubuntu / gcc-test (ubuntu-24.04)	8m 27s
ubuntu / clang-sanitizer-build (ubuntu-24.04)	3m 24s
ubuntu / clang-test (ubuntu-24.04)	8m 25s
windows / msvc-test	4m 54s
windows / clang-test-extended	3m 26s
ubuntu / clang-sanitizer-test (ubuntu-24.04)	2m 51s
mac / clang-test-extended	3m 6s
windows / msvc-test-extended	2m 55s
ubuntu / clang-sanitizer-test-extended (ubuntu-24.04)	2m 42s
ubuntu / gcc-test-extended (ubuntu-24.04)	4m 35s
ubuntu / clang-test-extended (ubuntu-24.04)	4m 28s
ubuntu / gcc-build-codecov	7m 35s
perf / macos-clang-build-perf-stats	2m 6s
perf / ubuntu-gcc-build-perf-stats	1m 40s
pages / build-scoreboard	14s
pages / build-doxygen-xml	20s
pages / build-sphinx	38s
pages / deploy-pages	0s
	1h 29m 9s

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