Not only is she a complex character, but she’s also multiple characters.
Ignoring other witches who bear the Beatrice name (such as EVA-Beatrice) we still have Beatrice Castiglioni, Ushiromiya Beatrice, Beato (the one we all think of when we say Beatrice), Beato the Elder, Beato the younger, Yasu, Ushiromiya Lion, Claire, and if you want to get technical, Shannon and Kanon.
Hell, there is a freaking chart to keep track of it all
And that chart doesn’t even include stuff like Virgilia/Kumasawa being the first Beatrice (by creating most of the rumors and teaching Yasu “magic”) and Eva and Ange inhereting the title as EVA-Beatrice and ANGE-Beatrice.
All of that complexity doesn’t even delve into the personality or motivations of any of these Beatos either.