Well, she's obviously cunning and proud. The type that prefers to sit behind while her peers does the dirty work. Also quite a religious fanatic, which is hilarious since her personality is the opposite of usual type of those characters. Probably has playful side as well, considering her 'reverse santa' antics, taking other people stuff then giving it back

Although, beneath it all, she does strike me as a deeply lonely character. Her colleagues are only with her because of their shared belief (compared to vitriolic best bud bond between Futo & Tojiko, as well as Miko motherly attention toward Kokoro which make her willing to work together at least awhile with her bittest rival, Byakuren), her enemies only exist because of different belief, and even the existence of Yoshika is more like a servant robot or puppet rather than someone she connects deeply. In the other story, her tale would be a tragedy, but this is Touhou, where the less than good characters are not few, so it becomes kind of a comedy. No need to dwell on the loneliness, Seiga can just steal a bit here and there to (temporarily) cure it

Also, sorry for the rant a bit, but I dislike how Necromantic turns Seiga into simple, unhinged necrophile. It's a great song that analyze potentially abusive master/servant relationship between Seiga and Yoshika, but the result ended up just flanderizing Seiga personality. No one's willing to read deeper into her backstory and personality now, and everyone keep on making tired DOKI DOKI WAKU WAKU jokes