Using Outlook for Android in business environments for email and scheduling
I just solved same issue. I bought new Android phone, and I needed to add my Microsoft account. Doing it from Outlook app, I received an error after inserting the password, telling me to try again later. Same thing if I did it from Android Settings -> Account -> Microsoft account menu.
I solved installing the Microsoft launcher app, when configuring it, it asks for a Microsoft account. I inserted the one which was giving error in the Outlook app. In this one, it was added successfully. Also, it was now a Microsoft account present on the phone.
Returning to the Outlook app, it now saw it as an existing account, and asked me to add it. It didn't request the password again, as the account was already present on the phone.
I think the Outlook app miss some validation code present in other apps.