It only has 1st amendment problems if the courts care. Making abortion illegal is an ideological project that the majority of the current SCOTUS and their acolytes has been working towards for at least 40 years. If you think they're going to let the plain text of the constitution, federal law, or its interpreted tradition get in the way of that you have not been paying attention.
I have been paying attention :). For what it's worth, a handful of recent state laws restricting speech have been struck down by the courts (Florida social media bill) or are blocked from being enforced (Texas social media bill blocked by Supreme Court) or are in the process of being litigated (Florida stop WOKE act).
While none of those bills related to abortion, I'm still skeptical the courts would let this bill stand
