Looks like you may have made a decision already, but wanted to give Polaris a mention. Been using that on my home server, has a nice Web-UI and a mobile app on F-Droid as well.

https://github.com/agersant/polaris

I noticed I only got the rate limiting error when searching for an app on Aurora, but not to download and install. But how to get to the install page if you can’t search?

I opened Firefox/Fennec on mobile, searched for an app, clicked the result for the Google Play store. Once on the play store page for the app was open, I would choose the “Open in App” option from the Firefox menu and select Aurora.

That would launch Aurora and bring me directly to the App Install page. From there I could complete the installation.

This was sometime in 2023, but hopefully it will still be helpful today.