ci: add lychee links checker with cache

[PsiACE]

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Summary

• add lychee as a links checker with cache
• fix broken links

Fixes #14094

Tests

• Unit Test
• Logic Test
• Benchmark Test
• No Test - github workflow, cron: "00 18 * * *"

Type of change

• Bug Fix (non-breaking change which fixes an issue)
• New Feature (non-breaking change which adds functionality)
• Breaking Change (fix or feature that could cause existing functionality not to work as expected)
• Documentation Update
• Refactoring
• Performance Improvement
• Other (please describe): ci: add links checker

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This change is 

[BohuTANG]

It's weird modified the *.md files but all the CI will run :/ , should we improve it?

[PsiACE]

It's weird modified the *.md files but all the CI will run :/ , should we improve it?

Yes, we need to skip some files to avoid unnecessary resource waste.