As soon as someone starts to chat with an end user the request status should automatically be something like 'chat in progress'.
Thank you for sharing your idea! It’s open for comments and kudos, and we’re looking forward to input from the community. Once there is enough community traction, it will be further reviewed by the product team.
I understand this is for an OOTB solution, but have you tried using BR? It may be possible to detect the change and then change the workflow phase. How do you know when the chat is "stopped"?