The Graphene FAQ is a good place to start
https://grapheneos.org/faq#notifications
I don’t use very many apps, so I don’t have much experience to share. But I can say Signal works fine. I set K9 Mail to poll, to save battery a bit since I don’t need email immediately, but it worked fine with IMAP push.
I’ve been pretty happy with it. I tried Calyx first, thinking it would be nice to have anonymized play services. But Graphene is much more refined, in my experience, fixing some AOSP annoyances like deleting an SMS message that you opened from a notification leaving a phantom window in the quick switch list. And with my minimal app profile, I don’t find I need google play services at all.
The under screen fingerprint scanner on the Pixel 8 sucks, I wish they’d include face unlock or a rear scanner. It does seem to work better if I only have one finger registered, so maybe it’s a software issue that will get fixed. I know I should be using an unlock mechanism that’s something I know, instead of something I have, but I really don’t use my phone for anything I’m particularly concerned about.