Before you paint the stucco, apply a thick layer of High-Temp Silicone Seal between the stucco and the chimney pipe or anchor plate to create a flexible, water-tight seal that’s resistant to high-temps. Once it’s dry, it’s safe to paint.
Rutland 500-Degree RTV High Heat Silicone Seal | Clear | 10.3 - Ounce Caulk Tube
As for adding a 3rd layer of stucco… it won’t add anything to the performance of the oven, but it will provide an additional layer of high-strength protection. So when your daughters annoying boyfriend decides it would be cool / funny to walk on top of your oven, he’s less likely to come crashing through w/ that 3rd layer of stucco.