There’s a law that if you have US citizenship, you have to use your U.S. passport to enter and leave the U.S., and you have to live as a citizen while in the U.S.

I don’t think there is a law worded quite in that way, but the US does not recognize dual-USA+other citizenship individuals any differently than they do people who only hold USA citizenship. To enter the country you need to show you have permission to enter the country, and failing to show your USA passport can make them pissey. As a USA citizen, you cannot be denied entry to the country, but if you do not jump through the hoops they want you to, they can certainly make the entry take a very long time and be very unpleasant. Probably if you mistakenly hand them the wrong passport there will be no problem if you politely correct the error.

I understand that it IS illegal to have multiple USA passports at the same time, and I have encountered boarder agents who mistakenly have through that having passports from two separate countries is a problem - hopefully this gets cleared up quickly when they confer with their superiors, but it is much simpler if the issue never comes up. Possibly with better data integration between places, this is no longer an issue.