If you follow the full advice in the FAQ, as expanded here No App display in App Lounge - #4 by aibd will Anonymous login work correctly?
Please notice that Clear storage is required Clear cache is insufficient.
Is the problem just Google login? (I think you identify that.)
I think it would be good to know if Google login is a fail first … then second Paid apps can be a bit hit and miss, maybe depends how the money flows … thirdly, is it the particular Paid app(s)?
Be aware also of Settings > System > MicroG > MicroG Settings > Google Play Services and the note “experimental” re billing.