Rents tend to follow property prices but they lag.
Manhattan also has a big problem with the type of property that gets built, being ultra-luxury property (that sells for >$5k/sq ft). Part of the demand for this is parking money but there are other reasons. Insurance is a big one thanks to the infamous "scaffolding law".
But the main point I want to raise here is that politicians, regardless of party (in the US at least), have zero interest in fixing this problem. Why? Because they're all bought and paid for by the capital-owning class. NYC politics in particular serves property developers first, police unions second and whatever third is nobody cares.
A budget shortfall is built into your existence. This keeps you showing up to work and diminishes your ability to negotiate (since walking away isn't an option). This creates a compliant workforce that doesn't hurt profits by, say, wages going up even with just inflation.
This is what neofeudalism looks like.