I used 3" of insulation: One box and some leftover from a friend who was also building a pizza oven. If you want to nerd out on the subject see my analysis based on measurements I made on my oven:
Surprisingly, when I changed the insulation depth to 2 and 4 inches and reran the equations the overall results didn’t change much. Most of the effect is in how long the oven retains heat after the fire burns down. There’s very little effect when you’re burning wood to maintain the temperature
You might burn a little more wood with 2" rather than 4" but I’m betting it wouldn’t be noticeable since most of the heat will be going out the big, open door in front.
My 2 cents. YMMV