Bump bun and firebase-admin in /functions/testapp/functions

Removes [bun](https://github.com/oven-sh/bun). It's no longer used after updating ancestor dependency [firebase-admin](https://github.com/firebase/firebase-admin-node). These dependencies need to be updated together.


Removes `bun`

Updates `firebase-admin` from 5.10.0 to 13.0.1
- [Release notes](https://github.com/firebase/firebase-admin-node/releases)
- [Changelog](https://github.com/firebase/firebase-admin-node/blob/master/CHANGELOG.md)
- [Commits](firebase/firebase-admin-node@v5.10.0...v13.0.1)

---
updated-dependencies:
- dependency-name: bun
  dependency-type: indirect
- dependency-name: firebase-admin
  dependency-type: direct:production
...

Signed-off-by: dependabot[bot] <[email protected]>

Author: dependabot[bot]