Unfinished large panel opening in outside wall
I would put some sheet vinyl in there to act as a moisture barrier and then reinstall one of those cement boards into the opening. Then get some stucco mesh and attach it to the cement board and then apply the stucco. It might take a layer or two to bring it to the right thickness. Once the top coat has been completed, run a shallow nap paint roller over the area to try and match the texture. You might have to practice that a bit.
I agree with @jsotola .... sure looks like a cat or doggie door.