Curiously there is a phenomenon in NY called the Classic 6, which is a large apartment in a very old-established building which has a separate, - usually tiny - room (often in the attic) apart from the flat itself for domestic helpers. But you need a really good real estate broker if you want to try that route because they are a bit off the beaten path and most brokers aren't used to dealing with numbers of Classic 6 apartments.
Finding any apartment in NYC right now is hard as hell, let alone the unicorn you described.
Either you have a tonne of money and can pay a professional to sort out your helper’s visa or simply forget it. Cheaper to live in a hotel / serviced apartment. If you were moving to the European countryside… maybe easier.