[Docs Site] Bump @typescript-eslint/parser from 8.37.0 to 8.38.0 (#23907)

Bumps [@typescript-eslint/parser](https://github.com/typescript-eslint/typescript-eslint/tree/HEAD/packages/parser) from 8.37.0 to 8.38.0.
- [Release notes](https://github.com/typescript-eslint/typescript-eslint/releases)
- [Changelog](https://github.com/typescript-eslint/typescript-eslint/blob/main/packages/parser/CHANGELOG.md)
- [Commits](https://github.com/typescript-eslint/typescript-eslint/commits/v8.38.0/packages/parser)

---
updated-dependencies:
- dependency-name: "@typescript-eslint/parser"
  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]