Who decides on Swiss work and residence permits — SEM or the cantons?

Responsibility is shared. For a non-EU/EFTA work permit, the employer applies to the cantonal labour-market authority, which reviews the case and issues a preliminary decision before forwarding the file to the State Secretariat for Migration (SEM) for federal approval. Because cantons administer much of the process, where you intend to live and work can affect the outcome. SEM does not issue visas: once the permit is approved, the cantonal immigration authority authorises the relevant Swiss embassy or consulate to issue the national (D) visa that visa-required nationals need to enter for a long stay.