> how does renting out old stock not increase supply?

Raw and overall housing numbers can be misleading by their nature. That is, they can be technically true while being false for many/most people.

    Declaration: Housing supply is increased!
    Actuality: Increase is only in homes for >$100k income earners.
    The declaration is true for >$100k.
    It is not true for most <$100k earners.

   (of those <$100k earners)
   There could be a very slight increase in supply for $80k.
   It'll be less, if any, for $60k earners.
   There is no increase in supply for <$40k (25% of US households).

Past that, there is a challenge in tossing around $250k and $500k houses as examples of anything. Those numbers are 4x & 8x over what typical-wage households can afford.

Generally, there is no affordable, reasonable housing for typical income earners.