[Docs Site] Bump typescript-eslint from 8.37.0 to 8.38.0 (#23876)

---
updated-dependencies:
- dependency-name: typescript-eslint
  dependency-version: 8.38.0
  dependency-type: direct:development
  update-type: version-update:semver-minor
...

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Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>

Author: dependabot[bot]