I started Free.ai as a weekend project with the same mindset. And a month in the work hasn't stopped. So I second this. Just find a good name, it helps.
If you want a certain app with a feature and the app isn't open source, then you may as well just clone the app and add the feature.
Claude Code and Codex (and other tools) have computer use and are perfectly capable of navigating, experimenting, cloning functionality, writing tests...
If the app is open source it's probably easier to just fork and add your features though. And cheaper.
Hell, I use the (closed-source) app Smart Audiobook Player and I wanted Audiobookshelf integration. I asked Claude, it decompiled the app, added the extra code, recompiled the APK and it works perfectly, syncing my book's progress with the server.
I could write something, but it would be "I told Claude to do this and it did, I'm happy", there isn't really much more detail to write about. What would you like to see?