I agree that universal health care should be solved independently from UBI (Yang supports opt-in Medicare For All).
Housing is a more complicated story; there's certainly a theory that landlords will simply raise rents in proportion to their tenants new ability to pay more. On the other hand, a stable income boost might make the housing market more fluid, giving renters more options to move when the rent goes up. I personally favor LVT to discourage rent-seeking, and there's a lot that could be done by removing zoning and building restrictions (multi-family conversions, etc) to make housing more competitive.