In Karate Kid, when Daniel reads the letter Miyagi’s holding while crying, he mentions that his wife died in childbirth at “Manzanar Relocation Center”. This means that Miyagi’s pregnant wife was thrown in an internment camp while he was fighting for the US Army in WWII
I feel the best interpretation for the Robby and Miguel dynamic is that Miguel is Daniel LaRusso but one who was raised and nurtured in the toxic Cobra Kai philosophy. He goes from being a nice and amiable kid to a jerkass. He is essentially what Daniel would have become under Kreese. Johnny only sadly realizes that he is perpetuating Kreese’s philosophy to Miguel too late.
Robby, on the other hand, is his father’s son…at first. He is a criminal, a fraud, a lowlife. He is Johnny. But he comes under the Miyagi-do karate. He becomes a good person, finds balance in his life, comes to appreciate hard and honest work. He is what (bully teen) Johnny would have become under Miyagi.
This fits brilliantly into the theme of father figures and how they can influence you in life - for better or for worse.