Adding some research so far: I have taken a look at the Pusher module, and will try that in a bit. Push notifications are not what I need right here, at the moment, but I can see a use case for push notifications in future, but only when the native client is not active. Looking for experiences and ideas, especially for native, as the posts on this forum about pushing content, as well as the modules itself are 2+ years. Thanks!
Adding another couple of findings: the Pusher module is web-client only, not for Native React apps.
I have got a basic version working by using the AppEvents widget, which has a timer function, but that seems to be very much logic for something as simple as a chat message. Nevertheless, since this is a simple research project, I will stick to that one for now.
Okay, clear! Thank you!