Is zakat obligatory on money paid for a real estate project to own a home, or is it considered a debt that must be repaid, and thus zakat is not obligatory on it?

You must pay zakat (definition) on the money remaining with you each year if it reaches the nisab (definition) (threshold) and has not been paid for the housing project, because it is still your property. However, if nothing remains with you, or if what remains does not reach the nisab, or if it is owed to the project beneficiaries as a debt, then there is no zakat on it, unless you have other money in excess of your basic needs that you can use to cover the debt. There is no zakat on what you have paid for the housing project, because housing is not subject to zakat on what is spent on it.