Should a pizza oven door for this oven form a seal or would a small gap between the door and the face of the oven be OK?
I know that the purpose of the door is to retain heat, but since mine as-is will just lean against the oven opening there will be a gap of an inch or two near the bottom of the door on both sides of the opening. The door does not have weights on the back to force it to lean in, so I am resting it against the oven with a slight tilt to prevent it from falling.
The pizza oven door as designed does not form a seal; there will be a small gap as you describe. It is more of a shield and does retain almost all heat.
Adding a fiberglass stove gasket will give you a seal. It should work especially well with your setup.
In general, iron or steel closures like this don’t provide 100 percent sealing—it’s why stove gasketing exists.