Seamless chat login for logged-in WordPress users

From the perspective of a user of the WordPress site, it's weird that they need to login to chat, when they are already logged-in to the WordPress site. If I think of other websites with integrated chat, I don't think it's ever the case that the chat window requires its own login. Ideally, when logged-in to WordPress, the user should be seamlessly logged-in to chat as well.

There would potentially be technical limitations to address, we'd need to look into the subject more deeply to evaluate feasibility.