NY's population is close to the same as it was in 2008 and hasn't changed since then.
Since the US as a whole grew during that period, NY's % of the US population has shrunk.
But there is no evidence people are leaving NY. NY has millions more people now than it did in 1960...…..
The population in New York is shifting - from Upstate to the City and environs. Many Upstate Counties have lost actual numbers since 2000.
Partly it is 'tax' and partly it's 'snow' (like in 10 feet in Syracuse most winters) -- but more it's the loss of the old 'giants' - IBM, GE, Kodak, Link, Endicott & Johnson, etc. The economy tanked. Young people want to live in the cities. And that is despite the Army moving an entire Division into Ft. Drum. However, the USAF closed several big bases.
On the flip side - fewer people = less light pollution and a massive return of forests and related critters.