Each state is different. But in the states where the question has been litigated the Courts have ruled that SoS have no responsibility to determine eligibility.
IOW, the state courts have ruled that the Article II requirements are non-enforceable at all. Period.
How, then, can those lower courts be correct?
Tell me how the eligibility requirements could ever be enforced, if the states can’t do it because they’re not federal, and Congress can’t do it because 3USC Sec 15 doesn’t allow Congress to reject electoral votes certified by a State, and the federal courts can’t do it because it is a “political question”.