I see your ingenious mayor is having another of those spasms of civic uplift he is prone to impose upon you.
I'm here to testify, it's not as bad as you may fear. We've been doing this is San Francisco for more than a decade.
For some years I've been confused whenever we visited my mother-in-law in Manhattan: "where does the food garbage go?" I asked. "What?' she replied. Now you will get to find out.
Really, it's easy. If you don't like whatever ugly kitchen receptacle the program provides (and you probably won't,) get one of these with a charcoal filter. Any number of vendors of kitchen equipment will be happy to sell you one whose appearance you can bear. Finding a suitable container just right for your kitchen could even be a status symbol.
The green bags, another commodity to buy, are themselves suitable for composting though not much else since if left in place too long, the food scraps seem to eat through them. I guess that's part of the point. I don't know if they are same stuff as the bags for collecting your dog's waste; I think those are more substantial.
And then you just dump the green bag in whatever larger receptacle is designated for food garbage (and maybe some garden clippings, though most of you don't have to deal with those.)
You mayor seems a difficult sort. If I lived there I'd be up in arms about his policing policies and would have deeply resented his changing the rules so as to run for a third term. But on food composting, he's on the right track.
I last resided in your city in the early 1970s when the place was an urban dystopia -- I loved it, but I was young and silly. It seems you are showing the rest of the country these days that sustainability not only can be achieved in a high density environment, but that cities can be good places for people and the planet.
Thanks, New York. I always did find the sprawl-burbs boring as shit.