Is it worth it to buy a bike that comes with puncture resistant tires, or add them later? Is it better to buy a bike that comes with puncture resistant tires, or get a cheaper bike that comes with worse tires and then get them replaced?

Don't decide your bike based on the stock tires. Tires are consumable components, and will not last like the rest of the components will. Tires are cheap, changing the frame or drivetrain is expensive.

Just ride the stock tires until they are worn out, then replace them with the puncture resistant tires, if by that point they are still important to you.

Many shops will swap out various components as part of a purchase anyway, so you can have your cake and eat it too.