In general, at the state level, you cannot prevent someone from going to another state even if you suspect they’re going to do something there that’s illegal in your state. Once you cross state lines, you’re subject to the laws of the state you’ve entered, and to federal law. Interstate crimes, like trafficking, fall under federal law, and that’s when the FBI gets involved. In addition, the drinking age policy was enforced, not by state law and not even by federal criminal law, but by the federal government passing a policy that restricts highway funding. Oklahoma could not criminalize traveling to Louisiana to drink “under age,” the feds had to get Louisiana to change their state law.
Texas can’t arrest you for flying to California to legally smoke weed. They can’t arrest you for going to Las Vegas to gamble. What they’re trying to do is make traveling while pregnant a trafficking type of crime such that existing the state while pregnant is a suspicious act.
The current SCOTUS has made some ridiculous rulings, so I wouldn’t want to gamble on this, but I honestly don’t think that it’s going to be more than political virtue signaling on an obviously unconstitutional law until the republicans take power at the federal level and pass a national anti-abortion law that permits federal agents to arrest patients and physicians in New York and California as well as having the sheriff do it in texas.