New York ends up being a problematic comparison point, because they were at zero restrictions until mid March 2020, so most of the infections through near the end of March were effectively a "no restrictions" test case. I.e. people testing positive late March were the highly symptomatic cases (because of limited test availability), so these were generally people infected 10+ days before, which means they were before any restrictions. Restrictions on mass gatherings happened on March 12th, but the stay-at-home order didn't happen until March 22nd.

What I'm getting at is that, if you want to use New York as a test comparison for loose vs tight restrictions, you're going to have a much deeper analysis to do, and a large portion of the deaths in New York were effectively resulting from a period when there were zero to minimal restrictions.