An issue I've run into earlier this week involved the Chromium-based new Edge version 84 in this case, failing to launch when running via any shortcuts with the error message:
The application has failed to start because its side-by-side configuration is incomplete. Please see the application event log or use the command-line sxstrace.exe tool for more detail.
If you navigate to the Edge install folder, on my system this is:
C:\Program Files (x86)\Microsoft\Edge\Application\ and check for a new-msedge.exe, and try running that. This seems to have resolved the issue. It looks like Edge was partially through updating itself when this was caused, possibly due to a crash or the system turning off while the update was being performed. Running new-msedge.exe seems to finish the update, it replaced the existing msedge.exe and removed itself.