I looked at the category types and there doesn't seem to be one that doesnt allow any glitches or exploits. Each category has something where someone could get out of bounds, skip a major story beat, bypass cutscenes, or go somewhere the devs didn't intend. Would it be possible to get a full glitchless category?

the "No Major Skips" subcategory is what you are looking for. some minor skips and glitches are technically allowed as long as they don't skip large areas of the game or go out of bounds. you can see what skips are allowed in each category in the guide document in the guides section