Under WiFi setting there is Intelligent WiFi option. In that option turn off the option circled in white ink in the attached screenshot. This will make sure that your WiFi doesn't turn off. Actually this feature is useful of its turned on as it helps...
The actual original leather case from Samsung for S22 ultra is the one shown in attached picture which is different from what you have. Probably the case that you have might have some material which might be hindering with the antenna of the phone si...
No issues at my end with any case that I have used. I normally use Samsung leather case or its Rugged series case with kickstand stand. What type of case are you using? Plus have you updated the OS to the latest andriod 13 version?