Stockholm is not car free by any standards. On the opposite it’s very car friendly.
Stockholm is small enough that it’s walkable with fast public transport connecting everything.
I don’t think it ever took me over 30 minutes to get anywhere, none of my friends drive in town but over half of them own a car so we are often traveling north for skiing, south for the summer, weekends in someone’s parent’s farm, but I have no recent memory of driving around town, there’s just no need, plus, no drinking, so it’s a nonstarter.