Anyone have experience breaking a less early and having landlord find a tenant?

I just re-signed a 12 month lease (new build in Gowanus) in May, but looking to break it in order to move into a new place with my partner.

My landlord says I must be the one to find a replacement tenant (they suggested I list on leasebreak.com). But claude is telling me that "Under Real Property Law §227-e, if you break your lease, your landlord is obligated to make a good-faith effort to find a new tenant".

Is that right? Another issue is that my landlord is offering the same exact unit in my building but on a higher floor for $350 less in rent. They're telling me I must list my apartment for my current rent of $4,245... which seems unlikely to rent if there's something going for meaningfully less.

Basically, am I effectively stuck in my place (assuming I don't want to pay two rents at once)?