I’ve never heard the question “do you drive,” only “what do you drive?” The assumption that every individual owns and drives a car is pretty omnipresent.

Maybe it's a local thing? New York, perhaps? It's definitely not widespread. It'd be a really weird question in most of the country (of course you drive)

There are about 3-5 metro areas in the US where a substantial portion of the population doesn't drive day-to-day by choice (NYC, Chicago, Philadelphia, maybe DC and Boston). I have heard "Do you drive?" asked in those places. Everywhere else, it's "what do you drive?" and "what kind of car are you thinking about paying a bank to buy for you?".

As an American in my 30s I have literally never been asked nor heard anyone else asked “Do you drive?”

That is something you will hear towny people in the UK ask now. Especially when asking young people who are absolutely putting off learning to drive a thing they will not remotely be able to afford to run.

Where I am, at least, the more frequent question is "What do you drive?". Some people are truly baffled when the answer is "I don't, really".

Same, where I live the moment I tell people I haven't owned a car in 2+ years they are baffled as to how I even survive.