Re: Serves Google right
NOTE: this is not a guaranteed solution, Google periodically attempts to stymie this avanue of access, but I've been using it for years with only two or three very brief interruptions in service.
Interruptions may become more frequent as others are doing the Aurora thing now. Up to now I've used f-droid & Aurora too but my latest phone is a murena one running /e/ os (thanks for the review Reg!) and that has it's own app for anonymous play store access. Google could take that as time to try harder at blocking anon access.
OTOH regulators do seem to enjoy getting their teeth into Google (long may that last). G used to publicly argue that if you didn't stay logged into the store you might miss updates and get pwned. Technologically that is a bollocks association and I think we have the regular hassling they get to thank for such specious arguments fading. So it could get easier to use the play store anonymously, time will tell.
https://www.theregister.com/2022/06/02/murena_e_foundation_phone_test/