Fixing the icon in an "installed" web app on Windows with Edge
If you install a web app and the icon is missing or weird, unpin it from anywhere it's pinned and delete the desktop icon.
In Edge, go to edge://apps and pull up the detail page for the app you're trying to fix. If there's a correct icon there, click Create Desktop shortcut.
Hopefully this will result in a shortcut with the correct icon. Then drag this to the task bar if desired.