Probably something new would have to be invented as there is no mechanism to send messages to the browser in plain html. Something equivalent of a form element but without the action attribute. It would be nice to have something like (spitballing)

  <some-new-form>
    <input type="hidden" value="fullscreen" />
    <input type="submit" value="Go fullscreen" />
  </some-new-form>

Oh please no, we barely got rid of the target attribute /: