DeletedUser495 True, I was meaning more for the paranoid who either don't trust AS (eg. compromised) or don't trust their release process or whatever but trust the source code that they understand. In that case either read the code and build it yourself or use FDROID and trust a wider community (including FDROID folks) to have built an audited code (or a code that can be audited even in the future).
Anyway, I think we all understand there are many ways to skin this cat and it's mostly a non-issue. What @raccoondad suggested is a really good way to do it too (assuming you trust AS is not malicious in general):
I would like to mention on the signature verification aspects, it would probably be fine to use Aurora as a update manager, but I'd avoid using it for first installs at the very least.
My understanding might be a bit wonky here so correct me if wrong, but Android model doesn't let you install separate versions/modifications of the same app as long as package name is the same (even in different user profiles). Assuming you haven't spoofed your hardware, both AS and playstore should in theory fetch exactly the same apk.
If this is correct, it in many ways answers (5) if you are willing to give play store a spin in a throwaway private space or user-profile. Eg just spin up a private space/user-profile, install playstore, install your app, go to main profile, "install" app again using AS, kill off the private space (or switch it off). Done! The second "installation" (done by AS) will just fail if it were trying to bring in a tampered/different app (signature mismatch etc covered in (5) in OP).
This means you don't even have to keep gplay in your main profile where AS is managing the updates and hence not even share the current set of installed apps with it or remember to cut off network access or disable it (point (1) in OP). All that'll be known is that at some point you installed some app foo. Whether you still have it, update it, uninstalled it etc should be unknown to play. If you used burner g-account (if you can get one) and vpn then it wouldn't even know it was you. The "bad" apps in point (3) will ofc id you to themselves and possibly to big-G, but that's covered in that point.
And now you don't even need AppVerifier, the usual TOFU will work naturally and fine! How is this not private OR not secure? Am I missing something?