Naw. Twee isn't a new word. It's an old one.
But, yeah, excessively cute, colorful... think fairies and garden gnomes.
To be honestly, I had no idea that the word had particularly negative connotations. To me, it just means cute, colorful, bright, that sort of thing. Think greeting cards. I've heard Di Terlizzi described a twee before, and that's always kind of stuck with me.
In any case, whatever word you want to use to describe it, Radiant Citadel's artwork is very bright and colorful. To me, this is pretty twee:
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