I haven't seen any complaints, but folks who set this up are usually used to having persistent notifications (I currently have 6) without Google services.

At least I replaced the one from my Matrix client with the UnifiedPush-enabled ntfy. Hopefully it'll replace Signal too at some point. KDE Connect? Why not. K-9 mail? I hope, but that would require JMAP or IMAP adjustments.

One option would be to install the distributor as a system app.

You can easily remove them. There are instructions here: https://docs.ntfy.sh/subscribe/phone/#instant-delivery