Him having calibrated slave collars is a bit of a narrative oversight/convenience that I won't mind as it serves the story (nondeath for carmine), and the mechanics of their logistics don't really impact their purpose. Souma must have known, but did Carmine know he knew? Did he instruct the other leader to tell him?

As for the collared, to preserve rule(face) of law, he could simply say they are 'imprisoned' for treason... The prison being more like the Palace, continuing to serve their duties now that they are more or less on board the isekai savior train. Who would know better?

What I'm sketchy on is how they assume a mercenary state will be willing to buy back its hostage armies after receiving payment, assuming that isn't all of them.

Losing a war during the beginning of an ED credits roll. The ultimate 'oof'.