Microsoft have dropped support for Outlook 2010 client connecting to Outlook in the cloud.
Take a look at this which might help.
When signing in today, I am not receiving my emails. In checking the Info in the File drop down menu it tells me that Upgrade in progress. It also has a second item for Upgrade Outlook Connector. Clicking on the Upgrade Now button doesn't do anything.…
learn.microsoft.com
You will need to remove your current Outlook connection and create a new one using the Exchange option.
As you know your email client is 15 years old so it's had a "fair innings" given the nature of technology and planned obsolescence.