Re: Is this the same Google
No, Google does it for cash and lovely data, but it also is the way they synchronize paid app purchases across devices. They weren't doing anything for our own good, but along with their data collection comes some features that most users will want.
You don't have to do that, though. You can use an app like Aurora Store (which is on FDroid) to access the Play Store. You can anonymously install offline apps, at least until Google breaks it, and you can use it to obtain APKs for commercial apps which will require your own account to purchase them, but not to install them. This may break if the app concerned expects you to have a Google account or uses it internally. For example, I installed an app that uses Google Play for in-app purchases, and that one was not going to be happy unless the system had a Google account configured. I avoid Google tracking whenever I can, and I find Aurora helps to make that easier, but there will always be some things you can't do if you're using Google's platform without turning on their spyware.