https://developer.android.com/training/permissions/requestin...
The Play Store lists these permissions:
* view network connections * full network access * run at startup * draw over other apps * prevent device from sleeping
The only one that gives me pause is "draw over" because it would allow the app to capture screen content, and that is only concerning because of "full network access" enabling it to send data. I'm not sure why this app would require _both_ of these permissions.
https://reports.exodus-privacy.eu.org/en/reports/com.actureu...
This one is huge though? You can e.g. imitate other apps' login forms and collect passwords.
In context of OP's concern regarding trust, it's this permission in combination with the special access which might give a scrutinizing user some pause. And the network permission grants access to any network endpoint — not just Google's services related to Play Store billing.