I am having the same problem with Outlook (New). Started on Sunday, Feb 9. I assume there was an app update.
One email account stopped working. Tried repair - did not work. Tried deleting that email account and adding it again. Would not let me. Now I cannot add any new accounts. Even tried on another computer with no active email client. Downloaded lastest Outlook for Windows from Microsoft Store. It opens and I try to add an account. Goes to a Microsoft Sign In pop-up that is not able recognize my Microsoft account.
I was getting errors that said I needed a password from my provider. No such thing. Then got error that I needed an app password from my administrator. Well I am the administrator. Tried my email password and Microsoft account password. Neither worked.
I guess we are all waiting for Microsoft to fix the app.