SOLVED: iCloud Alias Set-Up in New Outlook for Mac
For anyone who has struggled with this, it is possible. This is the workaround:
Sign in to appleid.apple.com with your iCloud alias and normal Apple ID password, create an app-specific password for New Outlook, and then set up your iCloud alias email account in New Outlook. I have been trying to do this for years. So far, so good. Everything works as it should.