I think Google is only used to send empty notifications to android and chrome devices, right? IOS too, maybe? Not that this nullifies your point about Google. There's just not much for them to collect if what I asked is correct.
This is my understanding as well. However even this requires you to have various google-parts installed on your phone. These can be fairly obtrusive with permissions and such.
My understanding is that Play Services sends information about the user to Google periodically.
Correct. And Signal’s .apk includes a Google library for cloud messaging, but that library also collects information about the user and sends it to Google, even if the user does not have Google Services installed.
Well you still need to trust that Google/your device manufacturer isn't simply reading everything on your device's screen.