This is the kind of shenanigan that happens when you use an OS that literally has third party advertisements in its start menu
This is the kind of shenanigan that happens when you use an OS where the widespread norm is to run highly privileged executables with full access to your home (and desktop) dirs in order to install software. Or really uses full filesystem mutability for package/software installation.
Because I'd be willing to bet a pretty serious amount of money that someone tweaked the Edge MSI installer/updater package and accidentally re-triggered the "First Install Icon to Desktop" step on upgrades. Edge updates very, very frequently and Boom, bug.