Richter and Rauch totally intended to make a second movie, but they had major problems with the studio exec, and the movie bombed hard when it opened.
I used to hear the Banzai-BTILC thing all the time, too, before the internet. Totally thought it was true, myself, until I went and heard Richter give a talk a few years ago. Turns out the only real connection between the two movies is him.
This is about how the script for Big Trouble in Little China was developed. It's weird and fascinating and I totally recommend any fan of the movie read it:
https://uproxx.com/movies/big-trouble-in-little-china-oral-history/5/
This is also a pretty interesting read, about the Jack Burton character this time:
https://uproxx.com/movies/big-trouble-in-little-china-jack-burton/