Is Koyabashi secretly OP?
Not secretly at all. Fight against Kimuin Kamui, dragon ranking battle and many other examples.
She actually has absurd magic affinity but she burned it out in fight against Kimuin and her mind is unnaturally composed when she is faced with danger. She can deny divine powers by just refusing to believe in gods.
I think she has some very hidden authority based power that affects causality and makes her more compelling.
I think Lucoa showed hints of picking up something about Kobayashi before, but as sneaky as she is, she will not show her doubts directly. Lucoa likes to rollplay as a silly horni bimbo, but there were couple of moments where you can see that is influencing things from the shadows.
Also, I can't remember where I saw this, but I think that her ancestor or parallel world version is a legendary king or something... I have to reread the comic and the numerous spinoffs.