Bump @typescript-eslint/parser from 7.16.0 to 8.20.0 in /api

Bumps [@typescript-eslint/parser](https://github.com/typescript-eslint/typescript-eslint/tree/HEAD/packages/parser) from 7.16.0 to 8.20.0.
- [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/v8.20.0/packages/parser)

---
updated-dependencies:
- dependency-name: "@typescript-eslint/parser"
  dependency-type: direct:development
  update-type: version-update:semver-major
...

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Author: dependabot[bot]