Genius Bonus: There is serious implication throughout the series that Miyagi's style is Goju-Ryu (Hard-Soft Style) karate. First of all, his family name is "Miyagi", the same as that of Chojun Miyagi, founder of Goju-Ryu. There is a blink-and-you'll-miss-it moment when you see a photo of Chojun Miyagi on the wall among the pictures of Miyagi ancestors. A lot of the techniques Miyagi uses and teaches are lifted directly from Goju-Ryu (which, considering that Pat and Ralph trained Goju-Ryu to prepare for their respective parts, isn't strange).
In Cobra Kai: Daniel mentions that kata is the foundation of his karate. Goju-Ryu is based on two kata, Sanchin and Tensho, formalizing the "Hard" and "Soft" aspects of Goju-Ryu respectively.