I'm finding conflicting answers on whether women face prosecution in Georgia. The sponsor of the bill says no, but the fetus is legally a human, and if you participate in killing a human, generally all the plotters are prosecuted. Some may receive leniency for cooperation, but they're usually not entirely off the hook. I also saw the figure "10 years" (vs. 99 for doctors) but I'm not exactly sure where I read it.
I see potential for people falsely accusing doctors.
I'm pretty sure you are conflating the Georgia and Alabama laws. In the case of Alabama law (as of last week), the provider is punishable as a class A felony, which carries a sentence of 10-99 years. The law is absolutely explicit that the woman on whom the abortion is performed faces no punishment and has committed no crime.
Under the Georgia law, anyone who performs an abortion after six weeks (i.e. the law says after the heartbeat, which is basically six weeks) or 20 weeks in the case of rape or incest, has performed an illegal abortion. Illegal abortions carry a penalty of 1 to 10 years under Georgia law. (The new law doesn't change the penalty for illegal abortions. It redefines what constitutes an illegal abortion.)
Where the confusion comes in from the Georgia law is that the Georgia law specifies specific bits of the legal code for Georgia will be changed, but in its introduction, it also talks about the personhood of a fetus. It is from that clause that all of the other hype has been generated, because people start from that and connect the dots, in whatever way they find most convenient to connect the dots. Some people manage to connect the dots in such a way that it ends up calling abortion the crime of murder.
Here's the thing. That particular way of connecting the dots really constitutes coloring outside the lines. Find me a lawyer who says a woman could end up with life in prison for getting an abortion, and I'll show you a lawyer who is receiving payment from an advocacy group, or wants to. It just isn't there. However, there is sufficient ambiguity in the actual words of the statute that we can say exactly who will be charged with exactly what. For example, the idea that women seeking abortions cannot be charged in Georgia is firmly established by legal precedent. However, that's legal precedent, not the actual text of the law. I can easily see a judge, even an appellate judge, saying that the precedent doesn't apply since it was formed under a prior statute, and at a time when Roe v. Wade was a defining precedent for abortion generally. I can easily see a woman being charged under the Georgia law (not the Alabama law, which explicitly says she can't be) for participating in an illegal abortion.
Summary: Give up on the online magazine articles, or the web pages of PACs, or of advocacy groups. Find what lawyers are saying about the laws. You'll find them saying that abortion is not murder, and that the pregnant women (probably) can't be charged in Georgia. I say "probably" because opinion is not unanimous among the authors I have read, even after dismissing the agenda driven authors whose purpose is to stir the pot, as opposed to telling the truth.