To be fair to the NYT, the position of "public editor" was pretty unique in U.S. journalism, you won't find it at the Wall Street Journal or the Washington Post - nor at the big international independent newspapers. When the political right radicalized in the U.S. and went on their current anti-science and anti-fact crusade they started using the public editor's findings against the NYT, which made it pretty predictable that they'd eliminate it.
BTW., Margaret Sullivan, NYT's former public editor, is now writing for the Washington Post.
I believe it's generally a hit-and-miss: John Broder and David Gelles are bad, while many other journalists at the NYT have high journalistic integrity.
Everything I've seen the past few years from the NY Times is profoundly counter to what you've just asserted, but, all I've had large exposure to is their miscoverage of Tesla and politicians I find interesting who are seeking to be the Democratic Candidate for President like Tulsi Gabbard & Bernie Sanders, and their miscoverage of the Democratic Party candidates they so aggressively advocate for in lieu of those candidates. Perhaps their Sports and classified ad sections are still of high journalistic integrity.