A New conversation button has appeared for me inside my tenant both on the desktop and on the web as shown. This is very much like the button you in the mobile experience of Teams.
One of the major challenges with conversations or chats in Teams was the simplicity that you could create new conversation threads. This simplicity was its own worse enemy unfortunately, because what you’d find is that people would post new message threads rather than posting to the current or existing one. Many users didn’t notice that fact and you ended up with many, many disjointed conversations. That reduced Teams chat benefits and effectiveness.
This New conversation button will ensure that any existing reply will stay in the existing thread and you’ll only get a new conversation by pressing that button. It also makes the interface between, desktop, mobile and web more consistent.
Look out for the New conversation button coming to your Teams environment soon.