It may be because you do not have the blizzard authenticator, the website found here, there is also a phone app. I can not confirm that this is the solution to the issue, but it worked for me. When I opened the editor and went to open a file to log in and entered my details, it immediately gave me a code (sadly I can not show you the code page, it is just logging in without it now because it remembers 'safe' locations) and I went onto the app on my phone and allowed the login. Not sure why it is like this, as the authenticator is only optional. I hope this helps.
I've never used the authenticator, and after logging-in once it worked just fine for me. I start the editor and can open any map normally.
Do NOT try to log-in when trying to open a map after just opening the editor.
After starting the editor, try to log-in at either the "File -> Open -> Blizzard" tab, or the "Manage Published" tab.
If that still doesn't work, the one thing that comes to mind is that you might have different usernames in different regions. I remember this was a thing when Blizzard got rid of a region (SEA I think) and I had to tell the game which of the usernames is my main account.
You have to open the game normally and go to each region, and check if the game asks you to confirm this. Either there, or when logging-in via the editor.
If that doesn't help, then I'm out of ideas.