Edge icon missing in taskbar  

Ah I see what you mean. I too also don't see the icon when I launch just the legacy version.

I believe it has something to do with the way edge used to be installed.

It used to be a windows store app, but since the app was replaced/moved when the new edge installer was run, the location for the icon was stored within the app itself. So since the edge app is no longer connected to the windows app store the icon won't show because the only reference to the icon it has is now in the Microsoft.MicrosoftEdge_ folder.

I guess Microsoft wants to do everything it can to make clear that there is a new 'Edge'. Similar to like how most people don't know that Internet Explorer is still on Windows 10, but it is not accessible except by searching for it.

In my opinion, its because of the way Edge was originally developed/installed on Windows 10. You might remember that edge used to have a transparent icon on the task bar with a blue 'e', instead of the white and blue icon.

Microsoft, although I'm not entirely sure where, stored that icon either in the program itself or in a edge system folder. So when the new Edge installer was run, it must have removed/overwritten the data for where this blue 'e' icon was. Since the location for the icon data has been removed/overwritten it just appears blank.

Maybe someone who hasn't installed the new edge yet may be able to explain where the blue 'e' icon actually comes from, but I suspect it was built into the windows store app.

Edge is no longer a windows store app, but is now a desktop app, that's why the location has changed to 'program files'.

I don't think a fix will be released for this as most people will only run the new Edge, but at least there is a fix for a pinned icon.

Had an issue before with an invisible icon on the taskbar. Think it was the Store icon. Might not work in your instance as of the unusual Edge installations. In settings - personalisation - colours - tick the box for 'Start, taskbar' etc., under 'show accent colour on the following surfaces'. Go to themes and change to another. See if the icon appears. If it does then change back to your previous theme. Worth a try.