Android data privacy - impact of google account?

Hi, I've always assumed that not logging in on an android device with a google account is a reasonable way to not leak too much private information.
Is this actually true?
Since i learned that FRP means google has access to some part of persistent unformattable storage in my device, in which it can store permanent identification data, i never bound my google account to any device again.
This for me meant also disabling almost all google apps apart from playservices, as i unfortunately still need them for some other apps.
I mainly use f-droid as app source and used aurora store for everything else that's not available there and netguard to block most connections selectively, apart from play services which have full access with screen-on rule.
Unfortunately aurora store seems to be on its way out, as it looks like google is beginning to implement counter measures, atleast that's what my impression is reading about it, and i've also not been able to use it anymore, for a while now and on different devices.
This means i'm now forced to use the playstore for updates and as a source for apps that are only available there. And this means binding my google account to my device.
For now i assume that google only has a shadow profile of me as -some user- (i'm trying to be privacy conscious everywhere else too) , but i'm not sure so:
will binding my google account to my device be any more detrimental to my desire for data privacy or am i likely already fully exposed anyway?

My gut feeling says, that there may have been situations where certain actions could already have resulted in correlatable data or that certain information that is accessible through different profiles i have on the internet might already overlap to an extend that makes this hopeless. So now i'm looking for other information to help me decide about this that is not just my gut feeling.