bringing disparate groups together under a single app

Yep, that's pretty much how I'd like to see it done. Similar to lemmy/piefed, where I can reply to your comment from different server. E.g. Fluxer have something like this in their roadmap, fingers crossed.

My, probably very bad, understanding would be something along the lines of a shared, decentralized API. Almost like a specialized internet that only serves the functions of the apps.