Repair Custom-Submenu after Wordpress and Plugin-Update

I need a Wordpress- and CSS-expert who can fix my website menu (particularly submenu) which doesn't work anymore after update to the latest wordpress version and update of plugins.
The first proposal should be for only bringing back the original funktionality. A second project could include further improvements of the menu (e.g. smoother anomation).

Since I only updated wordpress and plugins most of the code (such as css) should be still there, but
for some reason it's not active or functional.

I have some older backups, some of them created with the Duplicator plugin, but I don't want
to restore the old backups because the content is outdated as well some minor design corrections
are missing in those backups. Unfortunately there are no recent backups.
But I can provide the backup files if they are helpful for restoring the menu functionality.

I need the menu to be fixed within a few days, because my website is currently down because
of this, which shouldn't be a longer condition.

The following screenshots show the current situation and some mockups of how
the menu used to look like.

STRUCTURE OF MENU

The structure of the menu is as follows.
There is a main menu bar, and a submenu bar.
The homepage has only the main menu bar.
Every other page also has the submenu bar.
If we scroll down, then the main menu bar disappears and only the submenu bar is
visible with a simpler logo. The submenu allows navigation within one page.
If we scroll up again then the main menu bar will show up again.

I also do software development. But I'm not very familiar with php and wordpress,
so it would take me to much time to figure out what's wrong.
But I would expect from the person who accepts the project that it is somehow documented
what was wrong with the menu, so that if the same thing happens again I could fix it by myself.

I can see in the custom css code that the css for the submenu still exsits, but something must
be missing there or in another file / configuration.

As stated above, I need someone with good experience in wordpress, css, php who has
also experience with creating various menus and therefore knows what to look for here.
Of course I'd prefer someone who is confident that he/she can solve it quickly.

Kind regards
Harald