Part of me wonders if he'll just be hounded by Japanese bureaucracy/government, media, ect. and it's not really as ominous as it is trying to come across and it was being cutesy with the wording to make people worried.
...Then again "gravitational anomalies" that was mentioned a few chapters back kinda hints that there are going to some sort of ramifications to the crossing of worlds.
I'm guessing they're moving away from the heavy emphasis on a cooking manga and going for more slice of life and drama bits perhaps with romance thrown into there as well. I can't say that would be a bad thing, because having a concept like this and just... utilizing it for food... has already been done before (both "Restaurant to Another World" and "Isekai Izakaya") and kinda seems like a lot of wasted potential in this case.