make separate update.zip that includes F-Droid.apk
!5 (merged) adds the possibility of building an update.zip that installs the Privileged Extension, but that's useless without F-Droid itself. So there should be another update.zip that includes the official F-Droid-signed APK. I think we can make gradle just download https://f-droid.org/FDroid.apk then check the GPG signature. Then embed that into the ZIP. The easiest install option is /system/app, but that has the disadvantage of being completely overwritten whenever there is a system update. There is the /vendor folder which seems like it should be a place for installing APKs but I can't find any documentation of it at all.
Perhaps its not such a big deal if F-Droid.apk gets removed from /system/app. As long as F-Droid has updated itself, it would be present in /data/app. Hopefully Android wouldn't freak out when that APK in /system disappears and it has been updated in /data/app. If it just happily switches to using the one in /data/app, then this would cover most of the time.