Earlier quoted context omitted.
BLS is the federal government. Congress and the president have the entire data set produced by BLS. They also have state-level data and more. There are no statutes explicitly tied to U3. Click through all the links at the bottom of this report: https://www.bls.gov/news.release/empsit.nr0.htm
I mean using it as what's commonly associated with unemployment. There aren't any requirements to use U3, but the DOL uses it instead of U6. I think most people's idea of unemployment is closer to other measures than it is to U3.
That being said, the closest single metric to follow isn't any of the indices. Try prime age employment-population ratio.