That’s why we have the Bill of Rights: it’s meant to stop people from simply saying “the government needs this power so we’re going to give it that power.” It isn’t about creating rights, it’s about recognizing and protecting rights that have existed all along.
This is kind of a contradiction. What the bill of rights does is exactly to codify certain rights into law. There are a bunch of things considered a right today which aren't written into the bill of rights, and there are things codified in there that a lot of people don't consider to be "natural and universal human rights". Something doesn't become morally right by being written in the bill of rights, it just becomes a legal right. And of course, the US government can in some hypothetical scenario throw out the whole constitution and write a new one, making a whole new set of legal rights.
Of course, the above hypothetical changes nothing regarding what is considered morally correct, it just changes what rights are codified into law. In fact, the bill of rights is explicit in pointing out that what should be considered a right can change over time, and several of its clauses are therefore open to interpretation.
The whole "recognizing that right X exists outside the legal system" kind of falls apart when you look at the details. For example:
This is not something that was ordained from above and has always applied to every living person. It's a right the government has decided to give you. You can agree or disagree with it, but it's a right every american citizen has nevertheless. In other countries people have a right to housing, sick leave from work, or a certain number of vacation days per year. Those are rights that the american government has decided to not grant its citizens. Again, you can agree or disagree with that decision, but the fact remains that american citizens do not have those rights. Whether any of those rights in some sense "existed all along" (even though a lot of people don't have them) is a purely hypothetical question. The question with practical consequence is which rights should be codified into law.
It does not violate international law. It's specifically regulated by an international treaty that some countries are part to. Don't go around spreading disinformation, it's a bad look.