When navigating to a slide using the keyboard and focusing on the progressbar, then on a new "tile" using left and right keyboard buttons, the focus should not disappear
Same goes when navigating via the menu. Make sure the focus isn't gone.
Currently it isn't clear where focus is set when the progressbar and menu are used to navigate. Check for instance https://www.w3.org/WAI/tutorials/carousels/working-example/ for best practices. Some places the focus stays on the button and Aria Live reads. Other places the focus is moved to the entire slide.