To clarify, yes it's a single (split) phase panel, with a 3 pole breaker to protect 2 circuits, one is a 240V circuit (no neutral) and the other a 120V circuit. Both terminate in the same jbox, both circuits have grounds, not that that should really matter. Obviously the 240V circuit would be in adjacent breaker spaces. There is no 3 phase service involved, this is a question about 3 pole breakers, not 3 phase service. The fact that one is primarily used for the other should be irrelevant just trying to verify that that is indeed the case and that using one for this purpose doesn't violate the NEC in any way. The goal is to common trip the 240V circuit and the 120V circuit together, to both kill the box that contains these 2 circuits and the equipment they are connected to.
Any 3 pole breaker should be rated for 120V relative to ground or I don't see how it would ever be OK to have it in any service panel. Is there ever a case in North America where a hot leg would be rated less than 120V relative to ground that would merit manufacturing breakers for service panels that would not meet this specification? I also don't know of anywhere where split phase service exists in the US where the voltage relative to ground exceeds 120V(ish) either. I assume residential neighborhood transmission lines almost certainly do exceed this voltage and are distributed to those areas as split phase but they are never terminated that way, not that I have ever heard of.