For a browser, this is fairly straightfoward with an open websocket (something philomena can easily support).
The logistics change for mobile devices, though, as delivering messages to them generally requires integration with Firebase (the only provider that can do this, as far as I know).
As convenient as it might make things, I also have an internal resistance to developing features that make this site more addicting to use, and push notifications would probably be one of those things. Additionally, considering how underdeveloped notifications are in general here, it might not be the best idea to add them right now.
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