Not segrating people improves the world. Segragating them introduces division, self-evidentially. Something to be avoided, then, and worked against.
Planners will try to mix properties in a new development, if the local politics is to provide for everyone fairly.
Answering your question: yes, I believe not being able to afford housing categorizes a person as poor.
“Provide everyone fairly” is a touchy subject and depends on how limited do you want your goverment to be. I’d rather choose where to live myself, based on my own means.
What planners need to do it make sure that when the rich vacate the neighborhood they left behind is good. Part of that is making sure that some of the rich decide to rebuild their current house instead of leaving thus mixing the neighborhood a bit.
Cities are a long games. The "ideal" state you plan today to build tomorrow is not the end state. That means your plans need to account for change. New development will be old in 20 years, what then?
Possibly your statement: "You cannot mix a new development like that. Building a house is expensive, so only the rich and upper middle class can afford it. The poor always have and always will live in the houses the above lived in some years back and left for something newer." could be a bit of an absolute.