There are cars in inZoi, yes, but the “classic car” is a purely decorative item. Use the Zoi’s phone to use the app that lets you buy a car, as the drivable vehicles are similarly priced to the Classic Car and buying it to find it can’t be driven can drain your hard-earned savings (edit: If you wait too long, that is.) and force you to start saving from scratch.
Sadly, there is no drivable version of the Classic Car.