I believe both the PS5 and whatever nonsense string of Xs, numbers, and descriptors MS named this gen's console can do 144Hz output. I don't know how many games take advantage of that or whether that refresh rate is common on TVs.
60 FPS isn't even promised on PS5 Pro. Most graphically demanding titles still aim for 30 FPS on consoles, with any game able to support 60 FPS consistently worth noting.
What they said is true. There are some games with 120 FPS modes on PS5 and Series X, maybe even series S. That doesn't mean every game (or even most) are like that, just that the hardware supports it. At the end of the day you can't stop developers targeting whatever framerate they want.
Wikipedia indicates the Switch maxes out at 1080p60, and the newest Zelda only at 900p30 even when docked
https://en.m.wikipedia.org/wiki/Nintendo_Switch