sounds like silver polishing cloth. Often guitars and others are buffed like this. Buffing can produce abrasion to either dull or shine depending on what you want.
buffing and shining actually cut into the finish, very finely, generally in woodworking that's from course finish (like a paint brush) up by increasing grits. Each grit is actually producing fiber and finer scratches into the surface.
Dulling is the opposite, your going down to a tougher finish. Sandpaper is likely way way way too aggressive.
the other aspect is you can't work spot by spot. You need to buff the entirety to the exact same level.
it's your pot and I doubt a glaze is much different than so many other finished objects, though it's likely more akin to glass than anything else.
silver cloth, wet sanding, Mr clean eraser, steel wool etc, these all range from like 20,000 grit to 1000 grit. Using too low of a grit would likely destroy the finish by being extremely aggressive.
Those polishing pastes and compounds are just extremely fine ground glass or abrasive (silver polish at home depot)