GCM (now FCM after a change of ownership to a Google subsidiary) is a push notification framework which is commonly used on Android phones. MicroG is an open source reimplementation of Google proprietary userspace apps and libraries, including GCM, with more focus on openness and privacy.
What kind of information does Google get about me if I am using the MicroG version of GCM in conjunction with messaging apps?
For instance, from this discussion about the Matrix protocol:
The GCM data contains the "cleared" message i.e. sender, room name, message type, text and so on.
If you send an encrypted message, the GCM data don't contain the decrypted message.
If there is no data in the push, it is required to trigger a messages catchup (which is done by default).
from which it seems that it gets quite a lot of metadata over my messages, in addition to presence data (if my phone (identified by a unique ID) is on, which IP it has, and possibly also where it is), which would already be worrying as it is. And I guess that less privacy-oriented messaging apps such as Whatsapp share even more metadata.