Bump vite and @vitejs/plugin-react in /example (#725)

Bumps [vite](https://github.com/vitejs/vite/tree/HEAD/packages/vite) and [@vitejs/plugin-react](https://github.com/vitejs/vite-plugin-react/tree/HEAD/packages/plugin-react). These dependencies needed to be updated together.

Updates `vite` from 3.2.7 to 8.1.4
- [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/v8.1.4/packages/vite)

Updates `@vitejs/plugin-react` from 2.0.0 to 6.0.3
- [Release notes](https://github.com/vitejs/vite-plugin-react/releases)
- [Changelog](https://github.com/vitejs/vite-plugin-react/blob/main/packages/plugin-react/CHANGELOG.md)
- [Commits](https://github.com/vitejs/vite-plugin-react/commits/plugin-react@6.0.3/packages/plugin-react)

---
updated-dependencies:
- dependency-name: "@vitejs/plugin-react"
  dependency-version: 6.0.3
  dependency-type: direct:development
- dependency-name: vite
  dependency-version: 8.1.3
  dependency-type: direct:development
...

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