I would have loved to take advantage of this since my wireless earbuds were significantly better than the wired pair I had. Unfortunately, a little pop-up warned me that this was not available on Android 13 devices. I was more than a little annoyed, but also curious as to why this might have been the case.
Messaging and Notifications basically follow the same protocol. Even though I usually have notifications disabled, I go and activate it for anything I care about - News, Weather, Slack, Whatsapp (yes I have that silenced). Every single message pops up as a notification. Could be bank alert, Ring alert, homekit alert, whatever ... it just shows. So you can keep tab on things you care about, and if you are really needed, well you can pay and get on the full Wifi. And anyways you can iMessage to communicate if needed.
It's interesting what does and doesn't go through. e.g. Facebook notifications update, but not the content. I guess that's because they use the same channel as FB Messenger.