I actually use <button> with appearance:none specifically for accessibility. You get all of the benefits of a button's accessibility, focus, click events, normal tabbing, etc, and can use them for things like toggling an accordion of content or showing/hiding a mobile menu. Better than a div because you don't need aria-role, and better than a link because it is not taking you anywhere.

As pointed out up thread, developers and designers often skip using <button> because it is hard to style just right. Using appearance:none resets the style but not the accessibility behavior.