So, you are partly asking about the causal link between the practice of keeping properties vacant and rising rent, as maybe you believe there are multiple explanations and that's not the dominant one, but you do also seem to not believe that the vacancies are a thing in the first place, which is a lot easier to address.

FWIW, even without my having any prior knowledge of the correct terminology here--which is apparently "warehousing"--it took about 10 seconds to find a bunch of references to what is going on using the search query "new york landlords keeping properties empty renters". I have provided a spattering of results from different kinds of sources.

https://jacobin.com/2022/10/new-york-city-landlords-affordab...

https://nypost.com/2022/10/20/nyc-landlords-holding-60k-rent...

https://www.fox5ny.com/news/nyc-warehousing-empty-apartments...

https://www.thecity.nyc/housing/2022/10/19/23411956/60000-re...

https://www.businessinsider.com/why-cant-find-affordable-nyc...

https://www.reddit.com/r/nyc/comments/ygnh7o/new_york_landlo... (discussion of the jacobin article)

How have you previously tried to find evidence and come up short? Can you list some of your failed attempts to research this?