The problem with buttons in particular is that a <button> by itself does nothing. It needs to be in a form (like Submit) or have some javascript to make something happen when you click it. A link, however, navigates to a page when clicked, and can be styled to look like a button. It’s really better for accessibility to use the correct element for the job at hand so that screen readers and browsers do the expected thing. The editor’s Button block is not really a button. It’s a link.

You can ask at your theme’s support forum for the trick to getting the theme’s button (but it might be useless to you without a form or script), or how to style Button blocks (links) like the theme’s buttons. (in other words, for the theme to support the core blocks by styling them)