If that is your stance, then there is literally zero privacy anymore. Zilch.
If I’m walking down the street and somebody marks that one person walked down the street, does that invade my privacy?
In that case, how does the concept of privacy even matter anymore? There is none, and there never will be.
That’s impossible. The Play Store app doesn’t care about Sync’s cache. That was simply coincidence.
Cleaning the Play Store app’s cache on the other hand might help.