Whether the congresscritters explicitly based their bill on the 14th Amendment or not, it clearly grants them the authority to take this action, and not a single thing about it would be different if they had based it on the 14th.
You're absolutely wrong there. The 14th Amendment gives Congress the power to enforce the 14th Amendment and no more than that amendment. That means Congress can stop states from violating a woman's right to abortion. Even if someday in the future the 14th no longer protects such a right, and even if an unborn child were protected as a 14th Amendment "person", Congress could then --at most-- prevent state actors from performing abortions. "No State" means exactly what it says: No State. It doesn't mean "No citizen" or "No doctor". In other words, the 14th Amendment -- like most of the Constitution -- restrains *government*, not private citizens. It never has and never will give Congress the power to regulate the behavior of non-government actors. Which is why conservatives are stuck grasping at the straws of the commerce clause and playing let's pretend. So much for the lie that we just want to overturn Roe and send the matter back to the states. Yeah right.