The two halves sit flush together visually but are actually two separate <button> elements, so Tab focuses them independently, and only the arrow button carries aria-haspopup="menu" and aria-expanded.
Easy to confuse with a plain dropdown button, but the behavior differs. A dropdown button's whole surface is just a trigger — pressing any part of it opens the menu and nothing runs on its own. A split button's left side runs the most common action immediately ("Export as PDF," say), and only pressing the right arrow reveals the remaining alternatives (CSV, PNG, Copy link) as a menu.
Keyboard behavior once the menu is open — arrow keys to move, Enter to run, Esc to close — matches a dropdown menu exactly.