IMO whether abortion turns out to be a negative or a positive right depends on the laws in the country in question. In the US the legal status of abortion is currently up to the states. In the couple states where abortion is explicitly a legal right you have a positive right to an abortion. That is, the state will ensure you have access to one.

In most states it’s a negative right—the state guarantees that if you pursue an abortion you’ll be protected from people who might want to hurt you for doing it. Sort of like being protected from religious persecution is a negative right in many places.

So, to me whether abortion is a positive or negative right (or not a right at all) depends on the legal jurisdiction.