Apparently my Series X was set to 60 hz, no idea why. But setting the console to 120 hz kicked in the 40 fps mode and I gotta say, it feels pretty good (with motion blur turned off). I know Sony has recently been doing 40 fps games for 120 hz screens and it makes a bigger difference than the number suggests (vs 30).
Those 40fps modes seem like a nice innovation and good compromise between smoothness/responsiveness and picture quality. Unfortunately I don't have a TV to take advantage of it, though I've only got a Series S at the moment anyway!
It sits perfectly in the middle between 30fps and 60fps, which seems counter-intuitive as you alluded to. Thinking about it in terms of how long each frame lasts instead, it makes more sense. Each frame at 30fps will last 33.33 milliseconds (1000/30) and at 60fps will last 16.67ms. Split the difference and you get 25fps, which is how long each frame lasts at 40fps.
30fps can feel quite rough to me now and I'll always pick the 60fps option if it's available. I switched Forza Horizon 5 over to 30fps to see how it looked, but it felt horrible after being used to it at 60. I'd love to see how a 40fps mode would feel on that and hopefully it gets added to more games as time goes on.
I can deal with 30 fps, but it is not ideal. Do keep in mind that instantly switching is not really representative of the 30 fps experience. At least, my brain does get used to it after a while, making it completely fine to play. The instant 60 to 30 switch always is super jarring. For 30 fps I do need to sit further away from the screen a bit.
The only modern game I went with 30 fps on the Series X was Control, as the lightning without ray tracing wasn't very good (no window reflections or anything). For pretty much anything else it has been performance mode. I find high Resolutions a bit overrated anyways (given a game has good image quality and AA).
But 40 fps is surprisingly great. Sony has added 40 fps modes to Horizon FW, The Last of Us remake, Ratchet and Clank, and Spider-Man. God of War Ragnarok will also have it.
Anyways, I am glad I went for an HDMI 2.1 tv, as quite some games on next gen have used it one way or another.