The text of the Georgia statute you cited only uses detectable human heartbeat as an example ("including"), not a requirement for personhood.
> “Unborn child” means a member of the species Homo sapiens at any stage of development who is carried in the womb.
This would seem open-ended enough to apply to individual eggs.
Yes, an unborn child is as you state, but the state will count an unborn child in "population based determinations" only if the heartbeat is present. That's a big threshold, and it's my understanding that abortions in Georgia may be freely performed if no heartbeat is present, so it's in effect stating "no heartbeat = no personhood".
> This would seem open-ended enough to apply to individual eggs.
Hmm, not sure about that one. The definition of "unborn child" is not met if the gestating egg is not "in the womb."
No sources here cuz I just got home and I'm tired, but I swear there was some press recently(?) about IVF clinics fretting about egg storage/disposable for exactly this reason. I don't remember if anything came of it, but I think some IVF technicians were worried about going to jail if they, for instance, forgot to put an unfertilized egg back in the freezer and it went bad.
And then when you get to fertilized but non-implanted embryos, of course, that's when the "life begins at conception" crowd starts having their say.
The issue of fertilized but non-implanted embryos is already well-understood, as that is the entire basis behind opposition to embryonic stem cells and derived products. The interesting part will be to see how various religions will react if you tell them the fertilized egg will grow in an artificial womb.