After creating a record from a support conversation other Connect Actions are not working.
If you check the logs you see an error related to 'conversation.document.group' being undefined or "No live_group_profile found for undefined"
After creating a record from a chat the document is updated to that type of record. Since all records do not have a group field (OOB only the chat_queue_entry table does) the document.group is undefined.
A better way to get the live_group_profile sys_id for a conversation to use with the Conversation APIs is to just reference it directly from the conversation object.