It's all well and good to talk about what FCNY can afford, but the question is about what they use. The primary barriers for FCNY doing anything remotely militaristic aren't material - they're political. It's ironic, but FCNY is almost certainly dealing with the nega-verse equivalent of the "Right to Bear Arms" crowd, only instead of lobbying to let everybody have guns they're always lobbying against militarization. Which would be very effective - one of the reasons gun lobbyists are so successful is that just showing up and saying "No" is pretty easy, while showing up and advocating for a more measured approach has the issue of getting everyone to agree which measured response to advocate for.
I don't doubt they have equipment for Armed Response Units/SWAT or whatever (potentially even a very large amount of it if a brave politician tried to skirt the disarmament and had had the PR/spin to get it past opposition/ fearful voters), but I also expect that the frequency of usage of that level of firepower in the course of normal policing will have fallen dramatically (per capita, total is probably about equal) due to stuff like bans on personally owned rifles, gun registration, and other stuff that happens everywhere but America RL and really cuts down on gun violence.
I don't buy this at all.
The structural imperatives of being disallowed by treaty from having even a nominal military means that they are going to be heavily reliant on their law enforcement agencies for any sort of armed response, with a concomitant increase in dual-capability equipment.
Pre-existing precedent from the Old Country means that NYPD patrol officers already have a practice of carrying a backup longarm in their patrol vehicle for which they are qualified, everything from shotguns to selectfire automatics.
Switching from Mossbergs and ARs to the new German hotness and standardizing on it should not generate comment.
As for private use, the anti-militarization crowd are fighting the current of having Victoria committing atrocities less than a hundred miles away in PA.
They'd be just as effective in FCNY as the Right To Bear Arms people are now: noisy, litigous, futile.
Even if they managed to somehow get that kind of thing into law, who would enforce it? How are you going to stop black market ARs flooding in from gunsmiths in Newark across the Hudson to every citizen who disagrees? You end up with something in the mode of Prohibition, where people, including LEOs will brazenly flout the law and hide weapons in their domiciles. Corrosive to societal cohesion, dangerous to the citizens.
Its not that there arent strong reasons to want to regulate firearm access in a metropolis in normal times; there are. But these are not normal times.
FCNY cannot have survived forty years after the Collapse by ignoring public concerns.
I suspect that private ownership of arms is funnelled into membership of officially registered militias and passing some sort of certification. Basically an expansion of the existing RL NYC licensing scheme for owning firearms.