I had this issue too. I just switched from the new templates back to Buddypress legacy and it is now working to click the private message button and you can start composing the message to the user immediately. It is something in the buddypress nouveau template.
Hello, did you find a solution, to remove menu items, but keep the functionality? I just want to move the menu items to a new menu location, not stop using the features. CSS did not seem to work to hide the menu item, as it still put 3 items into the “…” extended menu on the user profile.