I really like the idea of just adding a nav item/link that goes to a page dedicated to messaging. Perhaps at some point we'll create a hosted page that does exactly that (e.g. maybe a custom "contact" or "FAQ" page where customers can ask questions, etc)
In the meantime, our users should technically be able to set up a dedicated page for this, and just embed our chat widget on that specific page :) but we are going to keep thinking about how we can improve the UX for this kinda thing!