Very likely that it will still exist. The internet shutting down won't completely erase the bitcoin network so, it will be stopped for a moment but will remain there.

That's why even if there will an internet interruption for a week. Transactions will be stuck and it will be back once again if any of those mesh networks or other solutions will make it back there to proceed.

Satellite technology is already there and it's not only Elon's starlink provides it.