Example? I heard of antitrust laws for corporations - and all the “Acts” that codify them.

What are the union equivalents? What aren’t unions allowed to do? Are there cases where unions have been sued by governments for breaking these laws?

In the US at least strategic industries are banned from striking. This happened to the railroad workers last year where the government passed a law that would take away their pensions if they striked. Reagan famously fired every ATC worker when they went on strike. There are many other laws too, in my state public unions can't strike over wages. Of course they just say they're striking about iother things and negotiate wages anyway but it does effect their messaging.