I wouldn’t know how to implement it properly, but would love to see someone pick it up 
For reference I had posted a feature request here as well: Add a data-tag-group attribute for tags
As mentioned there I believe the technical implementation would be more aligned with Discourse defaults if it wouldn’t be assigned a class but a data attribute as classes are usually applied for common styles, not for unique identifiers. Also, tags already have the data-tag-name attribute, so a data-tag-group attribute seems to fit right in.
For styling in CSS, there’s no advantage to have a class. It’s just as straightforward to declare styles based on the attribute ([data-tag-group: "group-name"]).
With respect to the id, I believe it’s actually the same as the name. See https://meta.discourse.org/tags.json