“Unhoused” is the preferred nomenclature.

“Unhomed” is the wrong tense and way to use when referring to someone in this situation.

“Homeless” makes it seem like they don’t have a home, which isn’t true, as homes are not always a structure and can be considered more of a concept.

Unhomed is past tense and still refers to them not having a “home”, which again, is not true and is generally seen as a demoralizing way to refer to their situation as if they don’t, or can’t build a home from the communities they find themselves in.

Unhoused is referring purely to the structure of a house, not the concept of a home. A house is a physical thing, whereas a home is where you make it, sort of thing.