Privacy effects of disabling notifications through Android settings
Push messages - what do they contain
What data each app receives via Firebase push notifications can be very different.
Some apps receive the complete message content as Firebase push notification to the user's app. In such a case Google can of course see the complete message.
Apps that handle privacy related content should use push notifications not as data transmission system. Instead they use push notifications just as notification for the app that new data is available on their own WhatsApp/Signal/... server.
Therefore for messenger apps I would expect that the push notifications may just contain e.g. a number the app processes and then knows that new data is available on the server.
Disabling notifications for an app
Regarding the question what happens if you disable notifications of an app in settings this also depends on the app:
The app itself can check if you have enabled/disabled a certain push channel. Therefore it is possible for an app to disable the notifications on server side so that no push messages are sent at all if you have disabled notifications for that app.
However a lazy app developer may not implement such a check. In such a case I would assume that all notifications are sent as before but just ignored by your device.