Privacy

Not quite. The Play store will be its own application. Which you can apply permissions to. Any application in the same space can still talk to the Play store. That's just inner process communication. So if any app wants to it can still talk to Google Play in that same profile.

When you're logged into the phone you have three areas that are separate by default, you have the main user, you have the private space, and you have the work profile. All three of these could have different Google accounts that don't see each other, they could have no Google Play and nothing goes to Google. It's up to you