Is there a new law for green cardholders to petition even if I’m not yet a citizen?

Not that I'm aware of. You have to a U.S. Citizen to petition for a K-1 visa for your fiance(e). If you are already married, you can petition for her as a Permanent Resident, but it will take longer than if you were a U.S. citizen.

Only USA citizens can petition their fiance. Of course, there may be other visas she is eligible for, but not the fiance visa.

No, there is not. You can petition for a spouse if you are a green card holder, but not for a fiance.

You may file an immigrant visa petition for your spouse, but they will have to wait for an available priority date. Typically it has been faster for someone to first become a U.S. citizen, but that is not always the case, as priority dates do change. However, as a green card holder you may not file a fiance visa petition for your spouse. You would need to marry her outside the U.S., or she would need to travel to the U.S. using an appropriate business or visitor visa.