Building a new house and renting the old one absolutely does increase the supply of housing.
But paper often neglects reality. A reality where it can be more profitable to simply hold the land rather than lease out the home on it. Where a constructive loss can improve tax savings. Where the intent is to have it vacant for some other perceived use or gain - like a vacation home, AirBnB rental, Pied-a-terre, or just letting the structure languish until it can be condemned and bypass red tape around teardowns/rebuilds.
Current incentives and structures do not mandate that homes are made available when someone buys another domicile. That’s one of the myriad of issues affecting the housing crisis.
So if building one unit of housing increases the housing supply by 0.7 units on average or whatever, then the same logic applies, just overbuild by 30%.