It's mostly 80 hz, very rarely 120. For vertical scrolling, you need to go quite fast to get to 120, to the point where you can't read the information on it anyway. Horizontal scrolling however is a lot more lively, reaching 120 on almost any movement.
24 48 60 and 120 fps videos play at 24 48 60 120 hz, while anything in between defaults to 60 (for example 60fps video on 1.25x speed on YouTube is displayed at 60hz, while 2x speed at 120hz).
Games that can do 120fps, run at 120hz, but some have issues with Fps stability (Wild Rift for example cannot hold 120fps even on low settings, it just jumps around 105 - the display however is locked in on 120hz - this seems to be an issue due to the way Promotion works on iPhones, which is different to iPads' Promotion, but it's up to the devs of the app to adapt to the new version).
Source: I've done plenty of tests so far with an app called Lock Launcher that lets me put both the fps (what the screen receives from the SoC) and hz (how fast the screen refreshes) into the dynamic island.
I must say though, even if the phone almost never goes to 120hz, it still feels A LOT smoother to me than my locked to 120hz Samsung S21FE, especially while browsing.
You can dm me if you want me to test any apps in particular.
Whichever one you decide to get, I would recommend going for the bigger version (Plus or Max), both the extra screen size and battery life are very nice to get for gaming.