Hi Crag and Takuju,
Sorry for the inconvenience caused by the issue. We received a few threads about the Outlook client have “connectivity” issue when the tenant has been upgraded to the “blue” version.
Could you help me to double confirm the following things (please feel free to post the result here):
1, The users encounter this problem when the tenant is upgraded.
2, Try the steps in the following articles : Fix Outlook connection problems after Office 365 upgrade and How to repair the connection to your Exchange Online account in Outlook
If the problem persists, I will help you to escalate this case to the next level. We are glad to help you in this case. Thanks for your patience and understanding.
Thanks,
Aaron Yuan