This is more or less how the "an update is available" notice already works (see https://update.jj2.plus), obviously with the difference that it doesn't automatically download and install the update yet.

Because the infrastructure is in place already, as you can see, an automatic updater is not super difficult to make, and may very well be included in the next version. It's more a question of "how do we want to do this" than "how do we do this" or "can we do this" at this point. Is it desirable that people's JJ2 installations are automatically updated? Should they get a choice or should it happen in the background? That sort of stuff is what's holding it back right now, not so much the implementation details.