They can, pretty much like in the EU. There might be some technical differences, but overall it's both "right to work and stay if employed"

EU citizens do have a special status for work and stay in Switzerland that is barely more strict than moving within EU.

Yeah, I don’t know about what is included in the bilateral agreement with Switzerland. But at least in EEA (which is EU + EFTA - Switzerland) you are free to work in any of the member states.