In the academic sense of the term, negative rights include the right to not have things done to you (e.g., to not be deprived of life, liberty, or property without due process of law).
Positive rights include the right for you to do something, generally as against others (e.g., the right to have food, healthcare, or education be provided to you by other people).
I'm not sure it is useful to try to categorize abortion rights, for similar reasons why it would be difficult to categorize the right to try and grab the only parachute on a crashing plane. Even if it causes injury or death to others, our general tendency is to treat positive acts of genuine self-preservation as a negative right, if only in the sense that we would never enforce a rule that prohibits the person from trying.
A funky brain teaser on the topic might be whose right of life prevails when a perfectly healthy person turns out to be the only match for 5 patients with failing organs, one needing a new heart, another needing a new intact liver, etc., who are each about to die if we don't kill the healthy person and harvest their organs for transplant. And would the answer change if this wouldn't kill the healthy person, but severely decrease their quality of life - such as involuntarily taking one of their lungs and one of their kidneys?
I'm against forced birth, but have to point out that there is the argument, whether realistic or not, that the parent can always give the baby to the foster care system once it's born, so their obligation would be limited to 9 months total.
Personally what I take issue with is the inconsistency of forced-birth laws in the absence of comparable forced-labor laws. In a world of ideal policy, maybe we as a society might agree that a person should be obligated to sacrifice their time and health for the sake of preserving or creating human life. But then it shouldn't be applied only to adult women who had consensual sex. Why shouldn't non-pregnant people be forced to tend a farm for 9 months to produce food for those who are starving, or to spend 9 months working 80-hour weeks at an emergency call center with no pay?
I suspect the answer is that the rights themselves are not the issue here, but rather the motivation to punish women who have consensual sex.