New Outlook won't let me add my outlook email account.

Here's the problem... I'm not trying to add an Outlook email account. My Outlook email account shows up just fine. Unfortunately, that's not the account that I use. My third-party email account (which I use) also shows up as if available on the left side of the screen. However, when I click to access it, a "Sign In" window appears asking for my username, which is actually helpfully provided on the sign in line. When this is entered, I get an error message that my username is incorrect. It's not incorrect, but for some reason the sign in routine will not recognize it as valid, even though up until today, old Outlook provided access to this account without so much as a hiccup.

Unfortunately, they seem to have gone ahead with the transition to New Outlook with the problem unresolved. Yesterday, Outlook worked fine, and I had automatic access to my third party email account. Today, with New Outlook in place, I'm locked out with no way to sign back into that account because the sign in bot won't recognize my username as valid even though it's the same one that worked fine yesterday. Why should I even have to sign back in?

Thank you for your solution, it worked perfect.

Though I didn't delete the Gmail alias, which I used to set up my Microsoft account,
I just made the @outlook email the new 'Primary Alias'.

When back in 'New Outlook', I just added the @outlook email address account - Voilà, it was a green tick and in!
The only thing needed to do then, was to re-sign into the Gmail account, and everything was fine thereafter.

But why Microsoft could have not made this issue clearer in the beginning is beyond me.

Anyway thanks @TinkerUK

I did same approach than you did, and same result. Success! :)

Thank Madpeaz for your reply. What you have done is is to clarify and finish off the trail I started. Between us I think this is now have it fully fixed.