Created attachment 120634 [details] Split button in window Breeze renders a Split Button correctly when it's on the window: it gets a frame with a visible separator between the main body of the button and the dropdown menu bit. But when a split button is on a toolbar, there is no visual indicator, so it's easy to think that the entire button opens a dropdown menu.
Created attachment 120635 [details] Split button in toolbar, un-hovered
Created attachment 120636 [details] Split button in toolbar, hovered
Created attachment 120637 [details] How Thunderbird does it
This appears to have been fixed at some point in the recent past.