Before you deploy logic app to production, create a new office365 outlook API connection and get it authenticated manually by service account owner.
change your connection by clicking on link - change connection (as seen in your screenshot)
Otherwise if you do not want to create a new connection, you can re-use the same connection by authenticating it manually by service account email and password.
just ensure to update display name to service account email ID to avoid confusion.
Procedure - click on API connections seen on left pane, select your outlook (office365) connection. Navigate to "Edit API connection"(left pane) below properties in General tab. update display name and click authorize. It will ask for account to authorize (use service account) and then key in password for service account to authorize. Please save updated configuration.
now your connection is pointed to service account.
hope this helps.