Is it possible to add an ID or class name when using the button shortcode?
The button shortcode doesn't have a parameter for a ID or class, unfortunately.
If you would like to add this you can use the HTML code of the button instead of the shortcode, which is working almost the same:
<a href="https://yourdomain.com" class="btn btn-primary" id="customID"> Text on Button </a>
You can replace customID with your own ID.
It is recommend to add HTML within a "Custom HTML" widget or within the text tab of the "SiteOrigin Editor" widget.
Hope this helps.