"My phone is really hot, is this normal or is it broken?!" is something I started getting asked by random iPhone-using friends over the last few years as they upgraded to a new model and then felt it sizzling.
But even then it was no hotter than my 16 Pro
I have one, too, and you're right that the heating is just what happens while it restores its data and settings and whatnot.
I believe it also re-scans your entire photo library to re-identify dogs, cars, people, etc. with whatever improved algorithm comes with the new chip/OS.
This happens every time you get a new iPhone. Depending on how much it has to sort through, it can take a couple of hours to a week.
I always leave the case off for the first few days.
One less core, and from the benchmarking it's clear that it throttles a fair bit earlier than the rest. Even worse its a titanium body so worse dissipation