Definitions are important. Anytime you see the word "person", it is not a substitute for human. Person is a "legal" definition, it can refer to corporations, trusts, unions, and even humans. You asked the question...
"Who decides personhood"
Let's clear up that question right way. A person is anyone or anything granted "person" status by our legal system... thus the definition of "person" is derived from the law and not biology.
In other words, there is no biological link between "personhood" and human, both are different concepts.
An entity with "personhood" status has legal rights and obligations according to whatever those legal rights and obligations are defined as.
In the past, slaves were fully human, but denied "person" status, thus while they might have had the human right to liberty, they had no legal right to expect the state to intervene on their behalf.
Today, the debate is when do babies have "person" status. The answer is, when the law grants them that status.
A separate question is when does human life begin and what constitutes life. NASA has defined "life" for purposes of space exploration, however, in this technology world, we may soon build machines that can meet the definition of life.
NASA’s working definition of life:
“a self-sustaining chemical system capable of Darwinian evolution.”
https://exoplanets.nasa.gov/news/1764/life-in-the-lab/?linkId=251784505
A related question is when does life become human life? The easiest definition is to apply NASA's definition to humans as a species.
If the people of Alabama want to grant "person" rights to embryos, you have no standing to deny them that right unless doing so would violate federal rights, then the supremacy clause would override Alabama law.
Your arguments are largely biased by the outcome you are trying to reach. You have a right to your opinions as do the citizens of Alabama.
In the US we are able to move if we don't agree with our fellow citizens to a state, whose laws we find more in line with our opinions.
But the key takeaway, person and human are different, human rights are derived from the Creator and are unalienable, personhood rights come from government. Typically, progressive liberals have advocated against human rights in favor of government rights (rule by the majority) as highlighted in the various 2nd Amendment legal cases, but somehow they flip that when arguing abortion.
Our country seems focused on "outcomes" instead of process. Pro-choice people only care about whether a woman has an individual right to have an abortion without protecting the rights of the unborn baby. Pro-life people only care about protecting the life of the baby without protecting the rights of the woman. This outcome-oriented way of thinking is exactly why our country cannot find resolution to its issues.
