My understanding of what happens in the U.S. is that they are 100% able to investigate the effects of mergers, acquisitions and other anti-competitive behaviour on the labour market. They consider things like wage fixing to be anti-competitive behaviour, which means workers are protected from some of the egregious things that can happen when companies collude. That would also include no-poaching agreements—
On April 22nd, 2021. See this statement in context.