I see some core team on this thread, so just wanted to say THANK YOU! Awesome job! Keep fighting for the users!
I'm totally the wrong person to offer recommendations on mobile, but so far it works very well for me, but then, I use almost no third party apps, and none of them are Play store only. My only complaint is the hardware (outside of their control).
After opening the application, it complains about being installed through an "insecure method", and bails. Reinstalling through Google Play magically fixes that.
These "security checks" are spreading like measles, so expect to see this sooner or later.
That's because apps that aren't published just on the Play Store but also on other stores or for direct sideloads (for users running Huawei for example which doesn't have Play Store) need to be able to detect the installation method to do updates on their own if there is no backing store.