I have successfully used anonymous Google accounts with Aurora Store for a year. For any paid Playstore apps (1 or 2), I have saved the Apk files from an Android tablet and side loaded them on my Pixel. Aurora can be temperamental sometimes with connections and finding apps, but does basically work most of the time.
Essentially my phone remains anonymous from Google, including its location tracking.
My query is, if I signed into Playstore with my Google account, what information regarding my phone do I give to Google? Perhaps the IMEI? Perhaps my location? Am I missing any other points?