"the swiss equivalent"

As OP explains, freedom of movement can't be stopped in isolation from the rest of the bilaterals.

(btw funnily Schengen is just about the border control, we're talking about freedom of movement which is a different thing, e.g. UK wasn't in Schengen but the freedom of movement applied to UK as well before brexit, tho I guess people use Schengen interchangeably)