When someone says "the UN did X" what really happened 90% of the time is that countries meeting at a convention which has been organized by the UN (and I do just mean organized, the decision to have the convention in the first place was again 90% taken by countries at another event and so on) decided that they'll do X

The UN doesn't really have any power to do anything, it's just a way to organize countries working on a series of topics in such a way that the staff and infrastructure needed to facilitate meetings are already in place instead of every new thing requiring a whole set up phase

Well, those who sign the treaty are choosing not to use it themselves. Those who don't sign the treaty... no the UN doesn't have any such power. They can kind of catalyze global pressure, though.

They have quite a bit of soft power.

People say that the UN is ineffectual, but they have managed to nag countries into better behaviour with a shocking amount of success. Whether that's "power" or not is debatable, but the end result is stuff getting done.