I don't have a video of it. But I can give an example of a menu! Franchise Mode and the menu where you change price for consessions!
Shouldn't matter which console it is (I'm on PS5), changing the price of french fries shouldn't lag, and it is lagging bad. More common I'd say if you want to swap players in edit lines, because it really needs to be done in slow motion to make sure the first and second players are switched.
it's not the end of the world, but the games themselves are not laggy. It's strange how a simple menu can be sooo slow.
I'm trying to think if there is a menu I would consider "as responsive as you'd expect", but most are noticeably slow. I have been somewhere in the menu where it felt better.