Register your apps: You'll need to prove you own your apps by providing your app package name and app signing keys.
Couldn't this also be verified with a challenge-response signing, using the key? Why should Google have the ability to sign apps of the developer, instead of it being an end-to-end deal? Perhaps they need to have the ability to slip in some additional code if the government so wishes?
Or perhaps there is actually a legit reason for Google to have those keys or I have a misunderstanding of the requirement?
Maybe F-Droid could relax that requirement if it were feasible to do reproducible builds. Then the developer could just deliver the package to F-Droid, F-Droid would check that it matches what they have, and then publish it. But that's probably not going to happen. Alternatively some deeper proof-based certificate could be devised, but that's even less likely to happpen..