As far as I can tell, there is currently no CSS class specific enough to allow me to customize the existing element with CSS. This is why I wanted to add the CSS class to the widget (in vanilla Discourse), so that I could customize the element with just CSS.
Is it possible to add an additional CSS class to an existing widget (as described in my post above) with a plugin? Can you do so without risking getting out of sync with the default version of the widget and missing future changes/enhancements to the widget?
Unfortunately, I’m not the admin of the site I’m trying to customize. While I think I could convince the site admin to add CSS pretty easily (assuming the class is added to the widget obviously), I’m not sure I could get him to use a plugin (especially depending on the risks).
(Thanks for bearing with me. 
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