Co-browse for Web Messaging is deployed via Messenger, meaning there is no manual configuration of the deployment snippet unlike legacy Co-browse for Chat and Voice.
As part of Configuring Messenger you'll just need to enable Co-browse and select any related settings you'd like. As long as your Messenger Deployment is referencing the updated configuration version and your agents have the new Conversation > Cobrowse > Add permission, you should see the Co-browse option available in the agent desktop.