Everything about the story is beyond stupid.
Bad faith can almost be taken as read when you're talking about violent criminals.
New York is an area with a huge population (getting on for 20 million), it'd be trivially easy for them to have a single small correctional facility (or more likely specialist segregated area within an existing one) dedicated entirely to male bodied prisoners who've declared themselves female.
I cannot for the life of me think that anyone with a half functioning brain thinks that housing trans women, unsegregated, in a female prison is anything other than a terrible idea. It's utterly senseless.
in much the same way as it's patently not feasible or proportionate for every public toilet to add a third category of convenience for trans toilet users, it patently would be feasible and proportionate for every global metropolis to have a segregated trans prison wing.