Microsoft is finally allowing Windows 11 to use clean icons for apps on the desktop if they were downloaded from the Store.

If an app icon appears on my desktop—ZAP! Gone. I now even hide my taskbar so that nothing greets me but a pristine wallpaper ...

This will solve the trouble you are facing with icons of websites you pinned to the start menu. Let us say you created a desktop shortcut using Chrome. And when you pin it to Start, the icon goes ...