Renting homes and building and selling homes are two different business.
Higherand higher marginal property taxes for owners of non primary residences disincentivizes owning secondary residences, hence disincentivizes renting, hence decreasing supply of buyers wanting to buy homes.
There will still be first time buyers or people moving, so builders should still have incentivize to build homes, hence supply should not cease to come online just because there are fewer landlords.