Googe Play Services - isn't it supposed to be named Google Mobile Services (GMS)? I think when people think Google Play Services, they think Google Play Store, which isn't required.
On my old rooted Pixel phone, I semi-de-Googled via ADB and/or blocked almost everything Google-related via firewall + hosts file. I left Google Mobile Services (GMS) for FCM. It worked.
The issue with FCM is that it knows which apps push notifications, when, and to whom (account-wise). It doesn't know the content of notifications, but knowing that you received a ProtonMail notification at a specific time is already sensitive metadata.
Some apps aren't honest about necessity for GMS/FCM. For example, Authy, keeps showing error every time I launch it because I don't have GMS on GrapheneOS phone, but it works without issues. It immediately notifies me when I try to add another device to Authy account.
This gives me an idea - open-source push notification service created with zero-trust policies to make sure the service itself doesn't log and/or store or even know which app pushes what and to whom.