After update Manager (Desktop Edition) shortcut is not working

[eko]

Just try to install again, but maybe first read:

Can't Install Manager on Windows 11 IoT Enterprise LTSC .msix not opening

It would be surprising to me if your version of Windows wouldn’t support MSIX format. Perhaps it’s an optional component that is not installed by default considering you are using specialized Windows build. However MSIX is glorified ZIP format. You can rename MSIX to ZIP and then unpack the contents and launch ManagerDesktop.exe.

Manager file .MSIX extension

Yes the .MSIX file is the correct file .MSI is a old extension, .MSIX is a newer one. There is what I found that should answer at least one of your questions.