This frame is an error, and is leading to a lot of unnecessary division imo.

Unborn people are unique because they are entirely dependent upon a mother to survive in a way that cannot be replaced.

The human right to life is not absolute, at least under current law: a person who literally requires your body’s metabolical processes to survive is not entitled to that, and so we have decided the provider has the choice to cease providing it at anytime, with the stipulation that at the time the decision is made, they cannot choose mechanisms to end it which unnecessarily harm the recipient.

Interesting standpoint, I've never heard that argument (I'm also not very deep into this issue just couldn't hold back my superficial 2 cents). But imo it does not really invalidate the opposite standpoint, it just rationalises one point of view.

In that same framework, wouldn't a hospital be also allowed to turn of life support as it sees fit?

This framework is relevant because it is the one used to regulate the legality of abortion under Roe v Wade. (Viability)

Also re: hospitals, this moral framework has no real analog given the nature of pregnancy being unique. If there were other phenomena where we could become biologically attached (without full intention) to others to sustain them through our own biological functions, then the same legal and moral frameworks seems like they would apply to those scenarios - but I am not aware of any such situations.

Why is it just metabolic support that is the qualifier here? A child is still very dependent on caregivers for years after exiting the birth canal, and in many cases a child remains dependent on the mother's metabolic processes when thy receive breastmilk. Why is it acceptable to kill the child before exiting the birth canal but not after?

I see the point that there is no single way to separate the unborn from its mother, while in all other cases there are ways that it can survive when separated (even though the separation might not be allowed).

Correct. In the future if we can extract a fetus safely (to both mother and child) and bring it to term then under current law abortion by termination would be illegal, is my understanding.

That still doesn't answer why killing the child is acceptable.

It does: the primacy is that a person always has the choice to cease providing metabolic support of another person. If you take this as primacy then consequential death as a side effect of exercising that choice is killing, for sure, but a distinct category of killing with regards to culpability. Analogies fail: abortion is a unique form of killing by ending internal biologically bound sacrificial life support, so it’s best to not reach for analogs.

I would say for full consistency with this it would imply abortion providers ought to take steps to not directly inflict harm, but practically speaking death is assured under this framework and so perhaps that falls onto questions of suffering vs painless death.

Edit: To be more direct, the killing is considered acceptable since the alternative is less acceptable: namely, that a person who is providing biologically, metabolically bound life support to another via an umbilical cord is not permitted to cut that cord of their own agency, under penalty of law.

That's an incredibly narrow definition of metabolic support. Providing food for children is also a form of metabolic support and it is certainly not acceptable to just stop feeding your children. That also discards the idea that there is another life in the balance here that has committed no crime that would be considered on the level of forfeiture of life and thus has as much right to life as the mother does.

I invented the term internal sacrificial biologically bound metabolic support in an attempt to describe the exact nature of the very specific fixed connection of a umbilical cord. Adjust the terminology to your liking, but anything short of a direct analog of a fixed, biological structure connecting the two persons in a host/dependent situation in which an act of agency would be necessary to sever it won’t be useful for the point of argument. I don’t know of any useful analog so this is why I think arguments around abortion should be had on their own terms without trying to draw on analogies.

Is it an interesting way of looking at things. It certainly helps to explain why some people have a need to first 'dedumanize' a victim by attaching an appropriate label to ensure that what they are doing is not done to a human being. It is an interesting idea, but I am not sure it is accurate depiction of reality.