There is also an EdgeUpdater.app that comes bundled with the main app and is installed in the user's ~/Library/Microsoft/EdgeUpdater/ folder (hence no password required), so I wouldn't think the AutoUpdate app is mandatory to install in order to perform updates. Download and install the new Microsoft Edge. from another edge (there are 4 different edge) from another mac user try from another edge profile (so not trying just 2 edge accounts on the same edge profile) after you cleaned (if you dont need such data) or you can move such folder to desktop and edge recreate all from 0. You may already have this if you got Office installed. The pkg installer also installs Microsoft AutoUpdate.app in /Library/Application Support/Microsoft folder, which you may or may not want.

Both preinstall & postinstall scripts send telemetry data. I noticed that postinstall script does some cleanup if you ever had an older version installed, so this might be good. To save the proxy, click the Apply button in the next window. Using this app you can even review the preinstall and postinstall scripts and decide if you want them to run. In the search bar, enter proxy and open the proxy settings. I have used it this way for a few days with no problems whatsoever. Use some app like Suspicious Package which allows you to extract the Microsoft Edge.app from the pkg file and then drag it to /Applications. MS Edge still requires administrative privileges to install on MacOS.

Microsoft edge on macos