In that case, is Google Play Services allowed to run in the background / unrestricted / whatever? It is the means to delivering notifications for most apps.
Agreed. I'd factory reset and see whether it improves things.
Under certain circumstances it's possible that the service is getting killed due to lack of memory, but the FP3 has 4GB of RAM so that shouldn't be happening. One could probably diagnose it with a detailed logcat. Unfortunately I don't have the bandwidth to help.
Honestly, no. Whenever I see late notifications its usually on a degoogled phone
Usually, yes. But there is one exception: GrapheneOS. Since it allows you to use Sandboxed Google Play services, notifications work just like on any other Android device, you just need to disable battery optimization for Play services. But unfortunately it is only compatible with Google Pixel devices.