These animals claim it is up to the "physician's discretion"

They are basically giving the individual performing the abortion the power to determine if the baby lives or dies. Of course they would reach that determination by working with the pregnant woman.

But since they are authorizing abortions outside of hospitals and legalizing them in "birthing centers" I am not sure that whoever is killing the "product of gestation" is actually a doctor or not.

Practically and fundamentally, There is zero difference between a woman making this determination about the child on the day it is born or the day it turns 12 at this point. That law reads like you literally have the power to kill it while only needing advice from your "physician" as a prerequisite..