I agree with the general sentiment that people without a permanent shelter need more action than we as a society currently give them. I also agree that the general trend of using new terms for known issues often confuses the conversation and is of negative value.
However in this one case I think the term "unhoused" is germane to this post. OP posted about public spaces, and included a picture of tents. The people OP directly refers to are unhoused, which is a specific subset of homeless.
If we somehow had shelters or other short term housing for everyone sleeping rough we would have alleviated the unhoused (which is what most people complain about), while not changing the homeless situation.