build(deps-dev): bump vite from 6.2.1 to 6.2.2 in /react-example

Bumps [vite](https://github.com/vitejs/vite/tree/HEAD/packages/vite) from 6.2.1 to 6.2.2.
- [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/v6.2.2/packages/vite)

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

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

Author: dependabot[bot]

react-example/package-lock.json

@@ -19,6 +19,6 @@
     "@types/react-dom": "^18.3.1",
     "@vitejs/plugin-react": "^4.3.4",
     "typescript": "^5.8.2",
-    "vite": "^6.2.1"
+    "vite": "^6.2.2"
   }
 }