Razer Kishi (xCloud) for Android - Smartphone Controller (USB-C Connection, Ergonomic Design, Analog Stick, Low Latency,) £36.53 @ Amazon

these days, every penny counts

Think the s23 ultra is too big. But don't think it'll work for ps5 remote play as it's Xbox configuration (edited)

Most of the ones with a USB-C connection won't, and even if they do the large tablet screen will extend below the controller (which personally, I don't like). I use a Nacon MG-X Pro with my Fold 4, and I find it great (more substantial than the Kishi I used with my old S10, and the MG-X non-Pro has spongy triggers)

Have you not tried Cex?

It does but with a workaround of having a Bluetooth controller connected to your phone, which is a little pointless

No controllers do on Android without messing about with screen mapping software that simulates touch inputs. For some reason the devs wont add it despite it being available on every other platform.

I am going to agree with @jrwagh333 here. Your original question and subsequent follow up for that matter doesn’t make sense. You say Xbox One as if you are talking about the console itself i.e. Xbox One.

After reading a few times, I assume you are trying to ask:
“This Xbox branded version of the controller does it work like a normal controller or does it only work for xbox cloud?”

If that’s the case, this controller is just like a normal controller which plugs into USB-C port. It acts like a normal controller and isn’t just for xbox cloud gaming. (edited)

S23 Ultra does fit if you remove the rubber pads, mine does. So if it's the same or smaller than this lump it should fit

The mount also works on the Stadia controller with a slight bit of filing the plastic to fit the USB-C port. I got the Travel and Charge Kit a couple of years ago which also includes a controller case, spare charge pack and micro USB cable.