GOS-user main goal is to prevent Google Serviced from working in the background and minimise their data collection and spying on me ;)
What's the concrete "spying" you are conceptualising here? As far as I can tell, you are using Play Store in a secondary profile with just one other third-party app installed. You can use a "burner" Google account for just this purpose. Then I struggle to see how Google could practically collect any personal information on you. It can get your IP address, but you can use a VPN to hide that. In any case, if you don't use your IP address for any other purpose, I don't see how Google realistically can tie it to you personally.
Please keep in mind that Play Services and Play Store on GrapheneOS are running in the standard app sandbox. It does not have privileged access and cannot do any voodoo stuff to magically break out of it.
I think you're simply causing yourself unnecessary inconvenience. If I were you, I'd just be signed into the Play Store and let it update the app.