I did some googleing and it appears many obgyns in the US give that to women with prior history of preterm birth (I haven't, DS was officially born at 37+2, since the ob changed my due date).
I talked to my sister in research (MD PhD in pharma), and she definitely told me to not take that stuff. Way too little studies have been done and none of the recent ones look at potential harm, only at if it prevents preterm birth. There are so many potential side effects of hormonal treatment, especially in pregnancy with a developing body and especially brain, it is to be taken very seriously and cautiously.
She also can't believe how little this obgyn believes in informed consent, not telling me potential side effects. They don't know how it works, it's been off the market in Germany for too many open questions, and on and on and on.
And of course, the obgyn will make money off of me as a trial participant. That's probably what she really cares about.
I ran away from this obgyn for many other reasons, and this was just one of it... In case anyone is offered this stuff, please be careful.