Prventh Thanks so much for the detailed answer, it gave me some food for thought. A good starting point for me might be to get a second a pixel phone to try it before a full transition.
If you're just dipping your toes, I'd suggest getting a Pixel 6a. It's a supported device with lots of life in it still (supported until 2027) and can be found for relatively cheap, especially used (make sure it can be unlocked!)
Prventh Let’s say I am using that ProtonMail app with notifications that require the google play service access in GrapheneOS. In practical terms what would be the difference to open and check emails in this app in GrapheneOS vs how it is currently on a iOS native app?
There wouldn't be much of a difference. You'd get a notification, press on that notification, and it would open the app.
Prventh Another question in this use case, how much more private is using this app in the graphene OS environment vs today on iOS?
Well, I don't know how the iOS app is, but using Proton Mail as a specific example, I can tell you how using an app like Proton Mail on GrapheneOS is more private than using it on Stock Android.
In Proton Mail, when you want to attach a file, the app brings up your system's file manager, you pick a file, and Proton Mail sees that file, and that file only, to attach it to your e-mail. However, if you receive an attachment, the moment you try to download it, Proton Mail will ask you to grant it access to your files. There's no reason it should do that, it could let you download it without that, or bring up the file manager to allow you to select a folder to save the file in, and it wouldn't only have access to that specific folder.
On Stock Android, you can choose to just not downlad/open attachments, or grant Proton Mail storage permissions. That's not the case on GrapheneOS due to storage scopes. Instead, by enabling storage scopes, Proton Mail thinks it has all possible storage permissions it asks for, but can only see files that it itself created, and nothing more. You can also grant it access to specific files/folders if you so choose, so that it can see those.
If you want Proton Mail to access your contacts, you have to grant it the contacts permission on Stock Android. It's all or nothing on Android. Not the case on GrapheneOS (this was actually shipped in the latest version, but has been in development for a while). On GrapheneOS, by using contact scopes, you can only grant Proton Mail access to some of your contacts, or to specific label(s) of contacts (essentially, what that means is that you create a label e.g. Friends, and add all of your friends to that label).
I think you might be noticing a trend here; control. GrapheneOS is about privacy and security. A lot of that comes in the form of under the hood hardening, but a lot of it is also easy-to-use features like the ones mentioned above that allow you to give apps the least amount of information.