Hi again.
So I've started from new MAX 2022 ENU folder and installed most of the scripts and made UI setting from scratch. This time I didn't install some of Sergo Pogosyan's scripts, but if you remember, I tried to remove them previously and it didn't help to solve the problem.
Max still works normally, I even worked with the scene, which as I supposed has problem point, but still didn't get this issue. So no clue where this problem was hidden. I'm happy that I can continue to work with the latest Corona builds, but maybe would be wise to understand what caused this Max behavior. If you need I can send you my new ENU folder, so you can compare it with the old one.