You can change elements of the website by adding a custom stylesheet to /opt/zammad/app/assets/stylesheets/custom. After you created your stylesheet you have to run zammad run rails assets:precompile followed by a zammad restart.
After that you hit F5 in your browser and you should see your changes.
I too modified the visibility of the menu items but not by changing the gray background but by changing the text and icon color slightly.
Here’s my menu customization:
It’s only a subtle change but raises the readability enough and still looks modern.
Please note: after updating from 3.4 to 3.5 the stylesheet was still present in the custom folder but my changes weren’t applied to the site any longer. I simply had to run the above mentioned command again to make it reappear.