Have you added the NewPipe repo in F-Droid? I get updates this way pretty quickly.

https://newpipe.net/FAQ/tutorials/install-add-fdroid-repo/

This issue happens to some extent within liunux distros too. I think specifically for youtube maybe it would be beneficial for a single core library that deals with the API and is shared by every single project that cares to interface with youtube. Rather than dozens of projects trying to chase youtube changes and overburdening repository maintainers, there would only be a single library whose updates would be fast tracked. This also requires there to be no embedding it in anything too, I don't know how feasible this would be on android/f-droid, but it kinda already happens with yt-dlp in linux distros, but yt-dlp isn't a proper library nor does it deals with all youtube endpoints that a proper youtube frontend would require.

It would perhaps be nice if yt-dlp could eject it's youtube api handling into it's own project that is then augmented to handle anything youtube related and turns into THE library for dealing with youtube.. maybe even call it libyt :)

I ran into the same issue. The good news is that app is the only one I've had to uninstall and reinstall from an apk because fdroid was so insanely slow. I wish they made an effort to keep up with apps where they need to be updated frequently and stop working entirely if they aren't updated. I can't imagine there are too many apps like that

True. And especially for that use, I can imagine that the slow return around is actually a breaking problem. I think there are relatively few apps that need that kind of quick update, and I'm more concerned with malicious authors than that, but it would depend on precisely what you need out of your apps.

I've never actually had this issue, for whatever reason. In-app updates to NewPipe (and the various forks) install just fine even if I originally downloaded from F-Droid. Not sure how that works exactly.