After 2 days of unsuccessful attempts to make some changes to the filtering listings form in the admin panel, I decided to test it in the original (unchanged) version of the script 4.9 and realized that this function does not work. But in the flynax demo it work. I don't know WHY, may be because my script is installed on local machine?

Please check if it works for you if any of you have installed version 4.9 on local machine.