Thank you for the responses!
As dazinism pointed out, just closing/swiping away Google Play Store from the Recent apps screen after checking for updates will not solve my issue since Google Play Services still tries to make connections to the internet (probably get "revived" from other installed apps calling them).
After some more thinking about the situation, my best way forward would be to wait until the "Install available apps" feature is integrated again to be used for the owner profile (it was removed again after being briefly included for some GrapheneOS releases).
This would allow me to have Google Play Store in a secondary user profile to install apps/ check for updates and transfer these apps to my main profile without having to install Google Play Services/Store in my main owner profile.
In the meantime I will continue with my current setup and live with Google Play services connections.