Make sure that your Microsoft account is associated with an Office login service and subscription. Check if it is actually associated with Office 365 and Office 2016 subscriptions. If your Office product is a Microsoft 365 subscription and not your email address, this will not work when you sign up for Office. Try to log in with your private email address if you bought Office with a different email address.
These bugs are not exclusive to Outlook.com as they have been reported for Windows 10, Windows 8.1, and Windows 7. It turns out that these errors often occur when users switch devices or use a single license or subscription, or when a company adds or changes Office 365 tenants.