what happens when I dial in an f stop of 22 on my old canon xti using a 200mm telephoto 3.5 - 6.3?
You have a fundamental misunderstanding of your gear.
When a lens is marked, say 55-200mm f/3.5-6.3, what that means is the maximum aperture you can use is f/3.5 at 55mm and f/6.3 at 200mm.
You can always stop down to any other smaller f stop* at any time.
** within reason here. Reason being the physical limitations of your lens. For many SLR lenses, that’s f/22. I had a Sigma one once go to f/32. Smaller than that is unheard of in the 35mm space.