So there is a company called Arcaspace whose launch vehicle gimmick is that by replacing the first stage boosters, which are generally either solid/cryogenic propellants with water/steam propulsion. They do this based on the idea that it's less polluting and cheaper. However from what I'm aware, water is also a greenhouse gas, meaning that it should count as polluting. And you generally need a lot more water compared to traditional propulsion because of low ISP. While solids and kerolox cycles emit other problematic chemicals, for this question the focus will be specifically on greenhouse gasses.
Would the greenhouse emissions of Arca water rocket be better/worse when compared to more traditional rockets?