In anycase, even a rate of ~.1% would be absurd given ~20% of people are testing positive by antibody tests.
I subsequently found what I believe you are working from here: https://www1.nyc.gov/site/doh/covid/covid-19-data.page which does specify New York City (as opposed to New York State) so both the numerator and denominator refer to the same thing.
Interestingly, they appear to be using a larger denominator than your 8.5 million (NYC metro vs. NYC proper perhaps?) and get a rate of 0.175% = 175.66/100,000, eg in the "citywide total" line of https://github.com/nychealth/coronavirus-data/blob/master/by...).
But this is at least closer to your figure than I was able to get previously.
https://www1.nyc.gov/assets/doh/downloads/pdf/imm/covid-19-d...
Specifically has numbers for NYC. You can sum the boroughs or use the total listed below. Using confirmed by pcr cases you get ~15k/8.6 = ~.175% as you said.
Using probable excess deaths adds an extra 5k deaths, hence ~.25%