Nothing, if you want. You can disable network permissions on play services. Google DDG first to make sure that won’t break the game. Depends on what the game uses play services for… if it’s some local functionality it will be fine, if it’s remote functionality then it will break.
Mullvad or IVPN. Some VPNs like Perfect Privacy do leak your IP via DHT and other torrent features, even when full lockdown mode is on. You can search ‘torrent leak test’ to verify yours doesn’t. I found out with a 2nd DMCA warning from my ISP.