I know it gets repeated here ad nausium, but taxing land would actually address this. Or if you can't do that because LVT is too memey, then just raise property taxes and dump the surplus on residents.

People who are foreign investors interested in buying rental housing will raise the rent to cover the increased property taxes. People who are foreign investors interested in speculating on vacant property (because they think that tenants are a risky way of damaging property or too much trouble to manage or they don't understand opportunity cost or whatever) will lose money and be forced to sell to someone who will build or at least rent out the unit.