build(deps): bump react-native

Bumps the production-dependencies group with 1 update in the /example directory: [react-native](https://github.com/facebook/react-native/tree/HEAD/packages/react-native).


Updates `react-native` from 0.75.4 to 0.76.1
- [Release notes](https://github.com/facebook/react-native/releases)
- [Changelog](https://github.com/facebook/react-native/blob/main/CHANGELOG.md)
- [Commits](https://github.com/facebook/react-native/commits/v0.76.1/packages/react-native)

---
updated-dependencies:
- dependency-name: react-native
  dependency-type: direct:production
  update-type: version-update:semver-minor
  dependency-group: production-dependencies
...

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

example/package.json

@@ -20,7 +20,7 @@
   },
   "dependencies": {
     "react": "^18.3.0",
-    "react-native": "^0.75.0"
+    "react-native": "^0.76.1"
   },
   "devDependencies": {
     "@babel/core": "^7.20.0",