Even assuming that there were no other federal, state or local YoY differences [1] that could explain this change (and that the numbers are right as presented in the first place), New York City private sector employment is
nothing like most other parts of the US: it's the largest city in the US by a large margin, it has a concentration of employment in a few major industries (finance, fashion, publishing, software) that aren't represented elsewhere, and...it hasn't been a manufacturing center since the victorian era.
You can't wave this away with "NYC is a leading indicator for the US economy". To the extent that it's true at all, you could say it about any large city in the US.
[1] Like, say: interest rates, the business cycle, AI, the slowdown in software hiring, or the minimum wage increase that NYC implemented on January 1, 2025.