I'm using MacOS and this is happening across the latest Beta (release candidate), Dev and Canary releases. When I click on "About Microsoft Edge" I get this error message "Sorry, Microsoft Edge update check failed." and if I open Microsoft AutoUpdate by clicking on "Open Microsoft AutoUpdate", it manages to check and download updates fine.
If I close the settings page and open "About Microsoft Edge" again, Edge says it's up-to-date (it's actually not!).
I've tried reinstalling Edge (and removing all the profile preferences), reinstalling Microsoft AutoUpdate itself. No changes in behavior whatsoever.