I don't think imposing sterility and such can be considered a serious topic, when we also have large political movements that are actively working to stop people from being able to freely control their own reproduction.
We know that providing affordable reproductive healthcare and free access to birth control helps significantly reduce pregnancy rates. There's no reason to be shady about it, at least not until we've tried offering the means to everyone, everywhere. And have educated everyone about it. Make sterilization free. Once we achieve maximum access to the means for people to willingly prevent reproduction, we'll be able to see if doing anything else is necessary. I very much doubt it, we have plenty of examples of countries with fertility rates well below replacement. They're not all China.