What kind of support is Morgana classed as?

I am trying to figure out a system to counter different types of support champions and I wanted to check whether I am understanding Morgana correctly. From what I've seen from video guides, there are generally four different categories of support champion: Utility, Engage, Sustain and AP. Each category is strong and weak against another category i.e. Utility > Engage > Sustain > AP > Utility. This isn't a strict rule but it seems like a good guideline, and each champion may belong to more than one category. Anyway, I think I can categorise Morgana using this system but it would be useful to hear another opinion. My first instinct was that she counts as an AP, but really I think in support because she doesn't itemise all damage and that she maxes q first, she seems more like an engage. However because of her shield and her aoe root, she also has some utility as well. I guess the question is am I supposted to pick and play Morgana as if she is an Engage champion that kind of counters other Engage champions (e.g. Thresh, Leona, Blitzcrank) because of Utility in her shield?
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