Some of the users have a need to use service account for the connection - some other account than the logged in user. However because of SSO, this does not work - even after providing username in the credential pop up, it defaults back to the logged in user. The workarounds are documented here - Integrate with Office 365 Outlook - Azure Logic Apps | Microsoft Docs
Also as a workaround, it is possible to use HTTP action with AAD authentication to call the Graph API directly.
One of the members from dev team has found a hack to get it working. For a good number of users, it has worked. If you are are reluctant to provide contributor access to the service account, it may be worth trying.
A user logs into Azure portal as firstname.lastname@example.org and he wants to create a logic app to send emails from logic app. He does not want the email to be sent from email@example.com and instead he wants the email to be sent from firstname.lastname@example.org. Logically he add the Outlook365 action to the logic app and then try to create the connection as email@example.com. The problem is that even though he specifies firstname.lastname@example.org on connection creation, the connection is still created with email@example.com. This is because AAD has the SSO feature, where AAD notices he has already logged in as firstname.lastname@example.org and it just uses that as the credential.