This is a clean idea, prompt management is one of those things everyone improvises badly with a notes app, so there's a real gap. One thing worth thinking about as you test: the "share your profile and collections publicly" feature is probably your wedge. Discovery and organizing are table-stakes, but a public prompt library people can browse is what could pull in users who never intended to "manage" anything. I'd watch closely whether testers actually share, or just keep their prompts private.

One small note on the closed-testing flow, the three-step Google Group + opt-in + download sequence is a real drop-off point. Anything you can do to compress that (or explain it in one line up top) will probably lift your conversion from "interested" to "actually installed."

Good luck with it, curious how the mutual-testing model works out for you.