Definitely a profile issue. So Android uses common app installs. This means that apps installed anywhere on the device (another profile, private space, etc.) are all using the same source of truth.
If an app is installed in one profile using play store, and you try to install it using f droid somewhere else, it will give an error. If you try to install an older version (that play store/aurora/f-droid may serve) compared to one that you have installed somewhere on the device, it will give a downgrade error even if they were installed from the same source. This does not affect apps that are not shared across profiles, so that explains why other apps work.
I would recommend removing installs in other profiles or using the main profile to push apps to other profiles instead of installing them from scratch if they are apps the device already has.
Seems like GOS will indeed work out for me when I actually get a new device and set it up such that Play Store and Play Services is fully operational and functional on the owner profile itself. The way I have been testing it is likely incorrect and hence the issues.