It could be a rumor or somebody's "guess" or "assumption" that in federally-subsidized housing, guns are not allowed.
I would want to see a rule or law that says so. With an actual citation to some authority like the chapter and section of the CFR (Code of Federal Regulations) or USC (United States Code). Not just some website or blog that says, in passing, "here's a list of rules for HUD homes" and you see on that list something against possessing firearms.
Congress has the power to make rules and regulations, and to delegate the rule-making power to agencies and departments in the executive branch, for all FEDERAL PROPERTY.
Is this HUD housing project federal property?
If so, did Congress give HUD or some other agency broad rule-making power?
If so, did the agency properly propose, consider, and then enact a rule in compliance with the Administrative Procedures Act?
If all that DID happen, then it looks like our Georgia statutory law won't matter. Federal law is supreme over conflicting state law on any subject where the feds have the authority to enact laws / rules.
I don't know how to determine if this is considered Federal property. The organization I work for is a non-profit and contracts with the State for clients. It is rather convoluted.