How can I make a clickable image in Bulma change the pointer on mouseOver like <button does>?

Bulma doesn't have a built-in class for that currently, unfortunately.

You can however easily create a class for that! To follow Bulma-conventions, let's call it is-clickable, and define it using CSS:

.is-clickable {
  cursor: pointer;
}

Now just include the class in the <figure>-element.

You can read more about the cursor-rule on MDN.