I'd go in this order. First, screenshot the StreetEasy listing right now, including the "no fee" tag, date, address, and broker name. In NYC rental transactions, a licensed real estate salesperson works under a broker, and they have to disclose who they represent. If they represent the landlord, the fee should generally be paid by the landlord unless you signed a separate tenant-agency agreement. If they represent you, they can charge you, but you would have had to agree to that—not find out by text after clicking an ad.
Second, contact the management company or owner directly if you can find them. Some buildings list their own leasing office. If the broker is the exclusive agent and the landlord isn't paying, they can still try to charge a fee for a lease they negotiated, but "no fee" should mean landlord-side. Ask in writing: "Is the owner paying your commission for this unit? Are you the exclusive agent?" If you hear "just pay the one month and you're approved," that's not clarity.
Broker fees aren't capped like application fees are, but they're negotiable. In a slower season or on a unit sitting, you can often get it down to half a month or get the landlord to split. You shouldn't pay anything except the $20 per applicant application fee before you have a lease in front of you. Never send first/security to a broker's personal Venmo. I've rented two no-fee places in Queens; in one I paid nothing to the agent, in another the landlord paid a month. The ads always matched. Walk if they tell you not to contact the owner.