Menu changes

you have assign that "other"menu to that certain page where it should appear ...

Ok, here is a different way to explain it.

Let's imagine, the home page will list a menu with these nav items:
Cities | Mountains | Lakes | Rivers

Then you would click e.g. Cities and a new page will be seen and the menu will change to:
London | Paris | Rome | Amsterdam

Next you click on Rome and the page changes and with it the menu:
Restaurants | Museums | Historic Landmarks
etc

I assigned a particular menu to a particular page, but pagebuilder does not honor the settings, see backend. Login credentials in hidden content.

do you use a "predefined header" on your page?
If so, you can't change the main menu on certain pages ... without using different template styles.

Go to the template layout-builder, turn off the predefined header, create a new row an call it menu and label it as modulposition "menu".

Create a modul for every menu you want to use and set them to modul-position "menu" and assign them to the page you want to have them ....