First, <button>
is not a link so any answers ascribing to what happens when you hover over a link don't apply. Second, CSS is a separate, independent specification from HTML. One does not specify what the other should do. It is the browser vendor that decides what CSS is provided for any actions in many cases though they tend to stick to the same thing if it's not in the specification.
It's been a long time since I've read this part of the spec and I'd have to review it for what is there but I'm pretty sure there is an indication nothing is to happen in this case because a button should be a button and if it's not a button it should be something else!