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

Bumps [react-dom](https://github.com/facebook/react/tree/HEAD/packages/react-dom) and [@types/react-dom](https://github.com/DefinitelyTyped/DefinitelyTyped/tree/HEAD/types/react-dom). These dependencies needed to be updated together.

Updates `react-dom` from 18.3.1 to 19.1.0
- [Release notes](https://github.com/facebook/react/releases)
- [Changelog](https://github.com/facebook/react/blob/main/CHANGELOG.md)
- [Commits](https://github.com/facebook/react/commits/v19.1.0/packages/react-dom)

Updates `@types/react-dom` from 18.3.1 to 19.0.4
- [Release notes](https://github.com/DefinitelyTyped/DefinitelyTyped/releases)
- [Commits](https://github.com/DefinitelyTyped/DefinitelyTyped/commits/HEAD/types/react-dom)

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

@@ -11,12 +11,12 @@
     "@db-ux/react-core-components": "^1.2.1",
     "classnames": "^2.5.1",
     "react": "^18.3.0",
-    "react-dom": "^18.3.1",
+    "react-dom": "^19.1.0",
     "sass": "^1.86.3"
   },
   "devDependencies": {
     "@types/react": "^18.3.12",
-    "@types/react-dom": "^18.3.1",
+    "@types/react-dom": "^19.1.2",
     "@vitejs/plugin-react": "^4.4.0",
     "typescript": "^5.8.3",
     "vite": "^6.2.6"