chore: Update markdown link check process and fix broken links

[nr-ahemsath]

The most recent markdown link check process detected some issues with recently-generated documentation. During the process of investigation we found out the the link linter we have been using has been deprecated since last year.

This PR:

• Replaces the markdown-link-check action with its successor Linkspector
• Fixes some hallucinations in Claude-generated documentation
• Ignore a link in the recently-created documentation on the CI performance testing system because it references a private GitHub repo.

Note: the main agent CHANGELOG is excluded from scanning because it was taking way too long. I don't think this is a problem since that file is largely auto-generated by Release Please these days.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 81.77%. Comparing base (24819c4) to head (24d1898).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3514      +/-   ##
==========================================
- Coverage   81.79%   81.77%   -0.02%     
==========================================
  Files         508      508              
  Lines       34220    34220              
  Branches     4040     4040              
==========================================
- Hits        27990    27984       -6     
- Misses       5265     5269       +4     
- Partials      965      967       +2     

Flag	Coverage Δ
Agent	82.76% <ø> (-0.02%)	⬇️
Profiler	71.75% <ø> (ø)

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see 1 file with indirect coverage changes

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