westwoods LinkButton is designed to handle an href. If the href is a path to a Flarum page (without domain, like /settings), navigation will be performed inside of the single page app. If it's an external link, the page will navigate to the new url, this might be what you experience as a refresh. Or maybe adding an onclick handler overrides the default behavior, causing the link to work like a plain HTML link.
If you want a button with an onclick handler, I suggest you use a Button instead. That way it won't trigger the navigation javascript when clicked.
You could also check whether your button has a type=button attribute. If it doesn't have it, clicking the button will submit a form as a POST request, causing a page refresh. https://html.com/attributes/button-type/ Normally buttons created through Flarum's components should have type=button added automatically.
