EEA gives you that, and Iceland is a member state of that too. So Iceland already enjoys this freedom.

I think Switzerland has a bilateral agreement with the EU (or via EFTA) that allows for free movement and employment of people, so they enjoy these freedom as well despite neither being in the EU nor the EEA (but they are a member of EFTA).

Employment too? I thought that was excluded. IIRC EU citizens can’t just work in Switzerland.

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.