They would use the hashed password to login to the server, using something like XOAUTH2. That’s the point of the hashed password. It accomplishes nothing other than revocation, which can be done already by changing your password.
I don't understand how hashed passwords got into this discussion though. My point is that microsoft should have no way to authenticate as an outlook user against their third party mail provider without the user explicitly giving them permission to do so and what they do is strictly unnecessary to provide the functionality of an email client.
Just like this comment I am writing is literally encrypted when it is send to HN, and still everyone can read it.
And yes, the issue is obviously that it is send in a way that microsoft can (ab)use.
> [...] tunneling [through an encrypted channel] back to their servers in plain text
Seems pretty clear to me. The message that is send contains the password in plain text. Any encryption that is applied in transit is absolutely irrelevant and meaningless. Just microsoft receiving the credentials is only marginally better than anyone getting them. In both cases the account will be compromised.