EDIT: Holy cow, this post got way, way longer than I expected.
The first step in the analysis is that, since no abortion law has been enacted by the US government, each State has its own set of abortion laws. Because killing a person is clearly illegal, the legality (not morality or ethics) of abortion hinges on when a developing clump of cells becomes protected under the law.
States have severe disagreement on that point. For example, consider the state of Georgia. The following is their definition of a person:
> There are two classes of persons: natural and artificial. “Natural person” means any human being including an unborn child. Corporations are artificial persons. They are creatures of the law and, except insofar as the law forbids it, they are subject to be changed, modified, or destroyed at the will of their creator. Unless otherwise provided by law, any natural person, including an unborn child with a detectable human heartbeat, shall be included in population based determinations. As used in this Code section, the term: “Detectable human heartbeat” means embryonic or fetal cardiac activity or the steady and repetitive rhythmic contraction of the heart within the gestational sac. “Unborn child” means a member of the species Homo sapiens at any stage of development who is carried in the womb. [2]
By law in Georgia, the status of personhood applies to a member of the species Homo sapiens at any stage of development who is carried in the womb with embryonic or fetal cardiac activity or the steady and repetitive rhythmic contraction of the heart within the gestational sac. The preposition "in the womb" clearly indicates a womb present in a human being, as it doesn't say "in a womb." As such, I do not expect legal personhood will automatically extend to a human being gestated in an artificial womb in Georgia.
On the other hand, consider the state of Massachusetts. The very beginning of their code is:
> All persons who are citizens of the United States and who are domiciled in this commonwealth are citizens thereof. [3]
Now, does the state of Massachusetts define in the state code what a "person" is? As far as I can tell, no, they don't (if someone else knows better, please chime in). A ballot initiative is trying to do that right now [4]. It seems that what constitutes a person in Massachusetts is less clear than in Georgia and is more a function of general consensus in society. As such, it's possible that a human being gestated in an artificial womb in Massachusetts would have legal personhood, and it's also possible that legal personhood is granted by governing authority. It's difficult to state.
What about at the federal level? The US code speaks on personhood as follows:
> [For the federal government], the words “person”, “human being”, “child”, and “individual”, shall include every infant member of the species homo sapiens who is born alive at any stage of development. As used in this section, the term “born alive”, with respect to a member of the species homo sapiens, means the complete expulsion or extraction from his or her mother of that member, at any stage of development, who after such expulsion or extraction breathes or has a beating heart, pulsation of the umbilical cord, or definite movement of voluntary muscles, regardless of whether the umbilical cord has been cut, and regardless of whether the expulsion or extraction occurs as a result of natural or induced labor, cesarean section, or induced abortion. [1]
At the federal level, the status of personhood is attained when an infant homo sapiens is completely removed from his or her mother.
So, by these laws, abortion becomes murder in Georgia after the heartbeat of a homo sapiens in the womb is detected, in Washington DC when an infant homo sapiens is completely removed from their mother, and in Massachusetts...well, it's complicated. Because the attainment of personhood is unclear, it's unclear precisely when abortion becomes murder. As such, Massachusetts specifically legislates when abortion is and isn't permissible without reference to personhood [5]. EDIT: In Wisconsin, before Roe and now post-Roe, abortion is murder.
So, on artificial wombs, based on current laws, I'd wager: Georgia will say you're not a person, Massachusetts will be the Wild West, Wisconsin says you're a human being but not born alive, and the federal government says you're not a person.
In my personal opinion, clear definition of legal personhood is the best approach, particularly because personal rights under the law stem from recognition as a legal person. From there, it becomes simple to state the precise conditions of when a clump of cells gains legal rights, be that at conception, presence of heartbeat, or live birth.
This is obviously hypothetical and should not be done, but I wonder if an evil company could exploit Georgia's laws to set up artificial womb farms and produce non-person human beings who exist solely as property. Georgia could easily prevent this by explicitly banning artificial wombs.
I believe these FOUR (not three, see edit) perspectives capture the essential elements of artificial womb legality across the USA.
EDIT: I kept doing some research, and Wisconsin's perspective distinct from those three:
>[Concerning an abortion]...“unborn child" means a human being from the time of conception until it is born alive. [8]
> Live birth: In this subsection, “breathes" means draws air into and expels it out of the lungs one or more times. “Live birth" means the complete expulsion or extraction from his or her mother, of a human being, at any stage of development, who, after the expulsion or extraction, breathes or has a beating heart, pulsation of the umbilical cord, or definite movement of voluntary muscles, regardless of whether the umbilical cord has been cut, and regardless of whether the expulsion or extraction occurs as a result of natural or induced labor, a cesarean section, or an abortion, as defined in s. 253.10 (2) (a). [6]
> An individual who undergoes a live birth is born alive. If a statute or rule refers to a live birth or to the circumstance in which an individual is born alive, the statute or rule shall be construed so that whoever undergoes a live birth as the result of an abortion...has the same legal status and legal rights as a human being at any point after the human being undergoes a live birth as the result of natural or induced labor or a cesarean section. [The preceding] may not be construed to affirm, deny, expand, or contract a legal status or legal right that is applicable to a human being at any point before the human being undergoes a live birth. [7]
Wisconsin doesn't designate personhood like Georgia does but instead says a human being comes into existence at conception and is born alive when undergoing a live birth or born during a failed abortion procedure. Note their "live birth" definition's alignment with the federal government's. However, an artificial womb in Wisconsin may create a situation where you're a human being but never born alive, meaning the definition of "unborn child" is not satisfied, meaning you can do anything you want to a human being created in an artificial womb.
Interestingly, the long-existing Wisconsin definition of "unborn child" was unworkable under the Roe v. Wade paradigm.
[1] https://www.law.cornell.edu/uscode/text/1/8
[2] https://law.justia.com/codes/georgia/2022/title-1/chapter-2/...
[3] https://law.justia.com/codes/massachusetts/2022/part-i/title...
[4] https://ballotpedia.org/Massachusetts_Definition_of_a_Person...
[5] https://www.mass.gov/info-details/massachusetts-law-about-ab...
[6] https://docs.legis.wisconsin.gov/document/statutes/990.01(19...
[7] https://docs.legis.wisconsin.gov/document/statutes/990.001(1...
[8] https://docs.legis.wisconsin.gov/document/statutes/940.04(6)