internal: Update stale link checker documentation #45508

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What article on docs.github.com is affected?

While working on #45507, I noticed that src/links/README.md still describes the previous rendered-content link checker.

The old rendered-content-link-checker.ts and rendered-content-link-checker-cli.ts scripts were removed when the link-checking system was rebuilt. However, the README still:

• References the deleted rendered-content-link-checker.ts script.
• Recommends running the unavailable rendered-content-link-checker-cli npm command.
• Documents obsolete options such as --level and --check-external-links.
• Lists LinkPreviewPopover.tsx without its current components/ path.

The current link-checking commands are:

• npm run check-links-pr
• npm run check-links-internal
• npm run check-links-external

What changes are you suggesting?

Update the README’s architecture, usage examples, supported options, component path, and performance notes to reflect the current link-checking system.

This should be a documentation-only change. I closed #45507 so the gap could be discussed and confirmed before proposing another update.

I may be missing context about how this internal README is intended to be maintained, so I’d appreciate confirmation that bringing it in line with the current scripts would be useful.

Additional information

No response