unable to add an existing email as an outlook.com alias

You cannot add an "existing" outlook.com address to another existing "outlook.com" address as alias, it is now supported, hence you would run into the "already exist" error.

When you receive the new computer, did you end up setting it up with a new outlook.com address? It is unclear to me why you are trying to add the old outlook.com address as an alias to another Microsoft account. It is unclear what's the involvement of this new Microsoft account? You said you bought Office, but you didn't mention why you ended up with a new Microsoft account?

On your Windows, if you go to Settings > Accounts > your info, is it listing your old outlook.com address, or is it a different one?

It sounds like you're running into a mix-up between signing into your account and trying to add an email as an alias.

The reason it's saying the email is "already taken" when you try to add it as an alias is because the system thinks you are trying to create a brand new email address. Since that @outlook.com address is already your existing Microsoft account, the system blocks it.

Instead of adding it as an alias, here is how you get it working on your new computer:

Open Outlook on your computer.

Go to File at the top left, then Account Settings > Account Settings.

Under the Email tab, click New.

Type in your existing @outlook.com email address and hit connect.

Enter your password, and it should link right up.

(Note: If you bought the Office suite using a different email address like a Gmail account, that's totally fine—Outlook allows you to add your @outlook.com address right alongside it as a separate inbox).

If it rejects your password, just head over to the Microsoft password reset page in your web browser to reset it for that specific Outlook address first, then try logging into the app again.