Could you elaborate on this? My current setup is like yours, I think. 3 Profiles (Owner app pusher, Everyday Use, and Google). I'm using Google Messages (Anonymously) in my Everyday profile because I like the enhanced features.
I only ever see "New message" in my Everyday profile, but I wish it showed the sender and message preview. Is there a setting I need to change? You mentioned using Private Space, but I haven't messed with that yet and don't fully understand it.