Weird. I just double checked and I do see "full page" as an option. I've used it but you have to live with the quirk of how it renders on device; I usually get the responsive design version of a site when sometimes I want the actual desktop version.
Do you have the most recent iOS installed? I believe it only works beginning in iOS 14. --I would assume so with a newer device. And, are you visiting a website that is longer than the screen? Again, I assume so.
I guess I'd try updating the device first. Then powering it down and restarting it (just for kicks) and see if that changes anything. Tried and true method for fixing errors. Short of that, I'm stumped.