Their coverage is much more complicated than left vs right, but one theme is they don’t question the loudest narratives, and they hold grudges when they perceive someone to not give them enough access.
The right tends to be louder and more uniform and persistent in messaging, so that coloring often gets unconsciously added to articles rather than the journalists taking a step back and analyzing the whole picture.
It’s the quick/lazy way to write stories after all, and journalists have deadlines. The author may be left leaning and some of that may even show, but a little left leaning flavor doesn’t mask that it’s based on the right’s take.
The choice of coverage also is very herd like, not left or right.
The NYT also goes out of the way to appear fair and balanced, trying to find the “average” in stories. But as anyone but the NYT knows, averages are skewed easily.