build(deps-dev): bump @types/react-dom in /react-example

Bumps [@types/react-dom](https://github.com/DefinitelyTyped/DefinitelyTyped/tree/HEAD/types/react-dom) from 18.3.1 to 19.2.2.
- [Release notes](https://github.com/DefinitelyTyped/DefinitelyTyped/releases)
- [Commits](https://github.com/DefinitelyTyped/DefinitelyTyped/commits/HEAD/types/react-dom)

---
updated-dependencies:
- dependency-name: "@types/react-dom"
  dependency-version: 19.2.2
  dependency-type: direct:development
  update-type: version-update:semver-major
...

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

Author: dependabot[bot]

react-example/package-lock.json

@@ -20,7 +20,7 @@
   "devDependencies": {
     "@db-ux/agent-cli": "4.0.3",
     "@types/react": "^19.2.2",
-    "@types/react-dom": "^18.3.1",
+    "@types/react-dom": "^19.2.2",
     "@vitejs/plugin-react": "^5.0.4",
     "typescript": "^5.9.3",
     "vite": "^7.1.10"