American cheese slices, Velveeta, Cheese Whiz, cheese spreads, nacho cheese are all NOVA group 4 ultra processed because they are industrial reformulations with added ingredients (like emulsifiers). Your average cheddar isn't.

And? For an "average cheddar" you still have to heat the milk, add enzymes, and age it and at the end you get something entirely different. Sounds like "processing" to me, or to use your words, "industrial reformulation."