We initially created the API before the update to allow closing of tickets but didn't finish the setup. We went back to it now and completed the setup and while tickets were created, if the alert was acknowledged in Sophos, it was not closing the ticket in ConnectWise Manage. I confirmed the API permissions we had set were the same as what was listed here https://docs.sophos.com/central/Partner/help/en-us/ConnectWiseIntegration/SetUpIntegration/ConnectWiseSetup/index.html and they were.
Under Service Desk there is a permission called Close Service Tickets. That had to be changed to All for the Add, Edit, and Inquire levels before tickets were closed automatically. The instructions may need to be updated to add that permission.