That seems... fine? I think there's plenty to complain about on Android (or on iOS), but this doesn't feel like a big deal to me.
You are already logged on your phone interface when you try to install so this additional check is excessive. I could have understood to have it just in the case that you don't protect your phone access with a pin.
Also, to not be anticompetitive, the behavior should be the same when using the play store or not. Like asking your pin to use the playstore like what is done in iOS. Even if it sucks if you want my opinion.
And out of the box, you can also install apps in our own user account without needing a sudo.
2. You installed Arch Linux. That is a much more technically demanding accomplishment that simply does not equal to enabling sideloading on an Android device.
3. The official Arch repos do not discriminate on the basis of whether a given package will harm corporate interests, or the interests of the Arch development team. Google Play does - for example, NewPipe, which is a far better YouTube client than the official app in many respects, yet Google bans it for commercial advantage.
If it requires a pin every time you install or upgrade from fdroid that would be really excessive and actively discouraging alternative app stores.
Just normal enshitification. Nothing to see here. /s
(maybe Google shall try to run Play Protect on the Play Store, i've heard that there is a lot of malware there)