samyak2403/RepoStore ? reverse-engineered prompt

Build me a modern Android app called RepoStore that feels like a clean Play Store for GitHub apps.

I want it to browse GitHub repositories that actually ship installable APKs, show trending, recently updated, and featured apps, and let me filter by category. Each app page should show the latest release, changelog, screenshots, repo stats, developer info, and the project README in a nice readable view. From there I should be able to install the APK with one tap, see download progress, and later tell if an app is already installed or needs an update.

Make it look polished with Material 3, dark mode, and a smooth modern layout. If possible, add optional GitHub sign in so the app can fetch more results without hitting rate limits. Also include a simple way to support developers with UPI and detect common UPI apps. Use current Android best practices, and look up any current docs online if you need to.