I am adding a new answer, since the old answer hardly applies to the current question anymore:
It seems more logical and consistent to have separate tags for each badge type.
I am not certain what you are understanding as a badge type here, but I created edit-and-answer-badges to serve for one badge type, namely the Explainer, Refiner and Illuminator badge (which is by now reflected in its tag-wiki excerpt). The tag is not intended for questions that concern both, edit badges and answer badges, nor is it intended for some future badge that somewhat concerns editing and answering. I named it edit-and-answer-badges, because that’s what these badges are about: editing and answering the same question. I might as well have called it curator-badges¹, explainer-refiner-illuminator, tims-badges or answer-and-edit-a-question-within-12-hours-badges.
I consider the tag consistent with the current badge-tagging system that has one tag for most complex badge mechanisms, whether they apply to a single badge or several ones. For example, we have tumbleweed-badge and do not tag the respective questions question-badges, score-badges, view-badges and comment-badges.
This tagging scheme makes sense in my opinion, as many questions around badges concern their mechanism and the mechanism is what people want to actually search for. For example, it is unlikely that somebody is explicitly interested in the Inquisitive badge and not the mechanism underlying the Curious, Inquisitive and Socratic badge, i.e., the asking-days-badges. But the latter is what people (including me) actually search for. For example, if I think I should have received an Inquisitive badge and didn’t, asking-days-badges is where I would look for existing information, because this way I also find information about somebody who had the same problem just with the Socratic badge.
Approaching the question of scope from the other site, e.g., most questions about the Good Question, Notable Question and Inquisitive badge are very unlikely to have more in common than being about badges in general and thus there is little need for question-badges to comprise all of them and only them. Taking the above example again: If I have a problem with the Inquisitive badge, question-badges would be almost as useless as badges for searching stuff about it. I rather run fulltext searches for
Socratic (which is tedious, since I have to search three times).
¹ which is in idea I only had later. We might very well rename or synonymise the tag, should we decide to keep it.