Currently you can start a new chat by first opening the AI Action Settings and clicking the green ‘+’ button. I think there should also be a new chat button in the chat panel itself because it’s a little hidden in that settings panel.
Also, I found the button to be a bit vague the first time not knowing exactly what it would do. I think having it say “new chat” along with a different icon like https://fontawesome.com/icons/pen-to-square?f=classic&s=solid would make it more clear.