chore(deps-dev): bump vite in /apps/browser-extension

Bumps [vite](https://github.com/vitejs/vite/tree/HEAD/packages/vite) from 8.0.16 to 8.1.3.
- [Release notes](https://github.com/vitejs/vite/releases)
- [Changelog](https://github.com/vitejs/vite/blob/main/packages/vite/CHANGELOG.md)
- [Commits](https://github.com/vitejs/vite/commits/v8.1.3/packages/vite)

---
updated-dependencies:
- dependency-name: vite
  dependency-version: 8.1.3
  dependency-type: direct:development
  update-type: version-update:semver-minor
...

Signed-off-by: dependabot[bot] <support@github.com>

Author: dependabot[bot]