I want to turn renters into homeowners. This strategy turns homeowners into landlords and puts more money in their pockets every month. Renters would hopefully see some benefit in terms of cheaper rent, but that only indirectly at best helps with the goal of turning them into homeowners.

Taking STR tax revenue and paying homeowners to build apartments transfers money from property investors to existing homeowners to build the unit, and then from renters to existing homeowners as the homeowner collects rent on the unit that potentially cost nothing out-of-pocket to build. Homeowners win 2x, investors lose (this is good), and renters also more or less lose (this is bad). So yes, I'd rather see the wealth transfer from property investors to renters, who then purchase a home. The property investors still lose (good), home sellers win (could be argued either way), and the (now former) renter has a home of their own to live in (good).

Or maybe the state should just take the tax revenue and directly build affordable homes that are deed-restricted to full-time residents with a preference to first-time home buyers. That's probably simpler, helps solves the supply problem, and helps first-time buyers. But if we're passing proceeds onto somebody in the form of a subsidy, then like I said, I'm firmly in favor of a plan that turns renters into homeowners, rather than homeowners into landlords.