I'm contemplating moving from an iPhone to GrapheneOS but I know, going in, that I will need to have Google Play Services installed with network access in my main profile. This is due to a work requirement and the need to receive push notifications and respond to them in a proprietary app that won't work without Google Play Services. While I understand the option of utilizing a separate work profile for this, the frequency with with I'd need to interact with this app would make it very inconvenient to be constantly switching profiles and, realistically, I'd just end up staying in the work profile all day. I use the same app on my iPhone currently and, obviously, I am signed into iCloud all the time. I don't use any Apple services other than the App Store.
So I guess my question is this: if I switch to GrapheneOS but run Google Play Services in my main profile, is there a net privacy gain over iOS? While I would be restrictive of Google Play's permissions, the network would necessarily always be allowed and thus a constant flow of data would go to Google (as opposed to Apple in my current situation).
As a secondary question, I've read up on the Aurora Store and its problems a few months ago when Google rate limited their anonymous accounts. I understand that they have successfully worked around the issue but I do have concerns that Google could eventually squash the Aurora store one way or another. In that case, those of us forced to use one or more proprietary apps would only have recourse to the Google Play Store. Again, I'm not too worried about that on its own but it does make me wonder if a move to GrapheneOS would be a long term privacy gain. Any thoughts?