Did some more troubleshooting.
This occurs every time I use a shortcut created in Edge (it does not occur if the shortcut is created with Chrome or Brave).
After it happens the "properties" option is missing when right clicking the shortcut (hence there is no way to edit the icon).
I can no longer create new shortcuts in Edge and then access the properties pane (and change the icon) this option is simply missing!
I also tried the "Open taskbar pinning wizard" that is available in Edge, but at the first attempt nothing happens and if I try again a grey window opens which seems to load forever and is impossible to close without going to task manager and close down Edge.
All this is the same if I star with Clean Boot.
To me it seems like this is a bug in the new Edge browser.