How much does it hurt my chances of admission if I have only taken AP exams and not SAT II exams?

There is room for school bias. Better school -> better teachers -> better AP results. I’d say that if you’re considered high-achieving in your specific school based on course rigor, you’re fine.

SAT subject tests would be beneficial, but shouldn’t hurt you too much (especially if you come from a low-resource/underrepresented school).