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Arent notifications same thing with only difference that they go through apple/google centralized server so your phone doesnt have to listen for multiple servers but just one?

A simple short-term workaround would a setInterval equivalent that can be set to "every so often" instead of a hard number, leaving it up to the browser or OS to coalesce updates into chunks of activity every so often.

background connections !== polling loops

Many services use an open tcp connection (e.g. websocket) rather than polling. Mobile platforms are doing the same thing, just on a system level. I guess service workers are the closest web analogue.