The new registration system is not the paid the full developer registration--that's only needed for Play Store distribution. The new thing everyone is complaining about is a different registration system that will be free (but likely requires identity verification). Google's announcement said that a solution was being developed but is not yet available to support individual and hobbyist use. They said it will be available before the system becomes mandatory (except for a few high-risk countries)

Frankly, I don't see why anonymous app distribution is necessary. The "I own my own device goddammit" thing is hobbyist category. Why should it be friction-less to install crap that has no provenance? That specifically seems like a really dumb hill to die on.

Besides making compiling apps yourself very difficult (you'd have to register and change the app's name), it's extremely likely that they won't just accept anyone and any app; at least things like NewPipe and Aurora Store are likely to get banned.

Compliling apps yourself would fall under and use the system for hobbyists Google said they are working on. At a basic level, apps you compile yourself would likely sideload over adb/USB and it's easy enough to exception adb as an install vector as distinct from app stores downloading and installing from the the network.

adb doesn't help F-Droid, but that's clearly a very different thing (at least as I see it).