chore(react-native): align the readme and the example app with the integration guide - #410

Node.js 20 is deprecated. The following actions target Node.js 20 but are being forced to run on Node.js 24: actions/cache@v4, actions/checkout@v4, actions/setup-java@v4, actions/setup-node@v4. For more information see: https://github.blog/changelog/2025-09-19-deprecation-of-node-20-on-github-actions-runners/

setup-java v4 is deprecated and will no longer receive updates. Please migrate to actions/setup-java@v5.