ci: replace markdown-link-check with lychee

[michaeladler]

Description

Replace markdown-link-check with lychee to reduce maintenance burden, as the current version has been broken for 2 months [1].

[1] tcort/markdown-link-check#369

Issues Addressed

List and link all the issues addressed by this PR.

Change Type

Please select the relevant options:

• Bug fix (non-breaking change that resolves an issue)
• New feature (non-breaking change that adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

Checklist

• I have read the CONTRIBUTING document.
• My changes adhere to the established code style, patterns, and best practices.
• I have added tests that demonstrate the effectiveness of my changes.
• I have updated the documentation accordingly (if applicable).
• I have added an entry in the CHANGELOG to document my changes (if applicable).

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 83.07%. Comparing base (aee20ca) to head (dbaabc3).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #265   +/-   ##
=======================================
  Coverage   83.07%   83.07%           
=======================================
  Files          97       97           
  Lines        4885     4885           
=======================================
  Hits         4058     4058           
  Misses        599      599           
  Partials      228      228           

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