I imagine certain parts of the NYPD would love an excuse to do that to Mamdani...

Yeah.

The NYPD has their own terrorism and counterintelligence divisions. They are pretty much an FBI governed at a city level (minus all of the cool forensics science).

I wouldn't put it beyond NYPD (in theory) except IIRC the NYPD actually drives him around in their SUVs and he has an NYPD team that does his personal security.