"An app downloaded from Google Play may not modify, replace or update its own APK binary code using any method other than Google Play's update mechanism."
It is still an OS level restriction too. There is no way to install an application without prompting the user except through "system" app stores currently. To test: you can install a vanilla Lineage OS ROM that does not have Google Play Services/Store, and then install the F-Droid application. F-Droid will not be allowed to install applications unless you (a) allow installing applications from untrusted sources (yeah, you cannot even say that F-Droid is the only trusted source, you just have to open it up all the way) and (b) you manually approve the installation of any APKs (including) updates that are installed via F-Droid.
