Keep in mind NYPD had its budget cut by billions of dollars and lost record numbers of officers over the same period. Part of accurate crime statistics is actually finding an officer to report a crime to and then them giving you the time of day. And that's if you haven't given up on the city already and aren't "mindin' yo own business".
I lived in NYC from 1984 through 2021 and I can tell you unequivocally that in 2021 it seemed more like 1988 than 2006.
If anything, the mid-2000s felt like the safest period of time that I lived in the city -- at the height of where a good party would be held in the same kind of places dead bodies would be dumped a decade or two earlier.