MichaelJohn Does that mean that private space is still in some way always transmitting data to the main profile (in order to update) or do the updates only happen when I open the private space?
No. Apps are installed "globally," so if the same app is installed in two different profiles, updating one means they're all updated.
MichaelJohn Also, if I ever want to install another Gplay app on my main profile, is there a way to "port" an installation from the private space, or do I have to install Google services, install said app, uninstall Google services again on the main profile?
There's no way that I know of to do that via the UI, unlike how it's possible to push apps from a parent profile to a private space, or owner profile to a secondary user profile.
I guess you can install the app in the private space first and use the private space to keep it updated, and install the app afterwards with Aurora in the parent profile. Keep in mind that some apps won't work without Google Play installed in the same profile and others may have less functionality.