This movie isn't a "reboot" — it's set in the same universe as the original Karate Kid franchise.
This movie isn't retconning the characters of Daniel, Johnny, Kreese, etc., but using entirely different characters in a different location who just happen to follow a similar storyline to the original movie. There's no reason to believe that the events of this film couldn't co-exist with the continuity of the original movie and its franchise. Jackie Chan is name-dropped in Cobra Kai, but you can just chalk that up to Celebrity Paradox. The real reason Mr. Han says what Master Li teaches isn't Kung Fu
Master Li actually learned from Kreese's sensei but, since he's teaching to his fellow Chinese, he calls it "Kung Fu" instead of karate for marketing reasons. Mr. Han just happens to be somebody who can tell the difference and cares about it. Practically everybody else just dismisses it as a variation of Kung Fu. Master Li's dojo will receive a life ban.
The people organizing the tournament in China are more strict than those organizing the All-Valley Karate Tournament in California and issued the ban without the need for Master Li to team up with a Chinese Terry Silver. Cheng will try to lift the ban in the 2040's but will fail and then decide to come up with a different name for the dojo to get around it.