How did Sento react to the "new world"? Or at the very least, Japan not being split in three, the currency being yen instead of dollarks and so on...?
Iirc, most of his (or rather, Katsuragi Takumi’s) pre-Sky Wall memories should have stayed intact even after Katsuragi’s consciousness went away, so maybe he does have a vague idea of things like that. He’d have a bit of an adjustment period but hey, it’s nothing too much for a genius, right? If anything, Ryuuga would be the one having a hard time since he already has little memory of his childhood, let alone what Japan was like pre-Sky Wall.
Additionally, in my own story, they were living with Shoutaro and Philip for a while. More than a while, really. That would give them some stability to get adjusted.
What they would have to struggle with is learning the history of the Japan they wound up in. And... that’s kind of a necessary skill?
Thing is, it wasn’t very clear how much of Build’verse!Japan’s history lined up with New World!Japan’s. The Sky Wall disaster was such a remarkable event in their history that it actually reset their calendar. So we don’t actually know what year Build takes place in Gregorian calendar terms. And just judging from how they already had the tech to send manned missions to Mars even before the Sky Wall went up, I’d say they’re at least a few years ahead of our ‘verse, if not decades.
In theory, if the New World is the Main Heisei Rider ‘verse, then it might be plausible that the timelines are quite close since the other seasons are a thing (like Kabuto, which confirmed the existence of alien lifeforms long before Build did it)... then again, one week in the Main Heisei‘verse was two years in the Build’verse, so...
(It does bring up the disturbing implication that the other Riders did exist in the Build’verse, but they were somehow unable to help deal with the disaster... because they were all dead before it even happened... or died as a direct result of it. But you know. MS3K Mantra.)