I am sure that someone here has the answer to my quest: 

I am creating an importable module, which is going well, but now I want to add a menu icon and I do not succeed at all.

The menu xml contains:

<menuitem .... web_icon="my_module_name,static/description/icon.png">...</menuitem>

What works

1. The menu works correctly with all actions etc. 
2. The web icon 'path' appears correctly in the menu settings once imported. 
3. My .zip file contains a file: static/description/icon.png.
4. If I search the module in the apps list - after importing it -, it shows the correct icon.

What does not work

1. On the 'home' page of Odoo, the icon is the ugly (V16?) empty box with exclamation mark. 
2. If I open the html (F12) and modify the path of the <img src=""/> form "/web/static/img/default_icon_app.png" to "/my_module_name/static/description/icon.png" the correct icon appears.
   

It appears as if the image is correctly imported, but somehow the path is not resolved correctly and as a consequence the 'default icon' is loaded.