Hello Kevin. I'm Greg, here to help you with this.`
There are a lot of complaints lately about Edge shortcut keeps returning to desktop after every restart, so it must be something that was pushed through Edge or Updates.
Most are fixing it by disabling the Edge startup listing in Task Manager > Startup tab which apparently keeps putting the shortcut back after every restart.
If not there check in Task Scheduler if Edge scheduled a task to run at every startup to put it back:
https://windowsreport.com/windows-11-task-sched...
(Avoid ad links which intrude into editorial copy, especially DO NOT INSTALL Restoro, PC Repair Tool and Reimage ads)
if you find the task In the list, highlight and delete it.
Feel free to ask back any questions. Based on the detailed results you post back, I will have other suggestions if necessary.
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