Well, I'm 51 and from So Cal and it would not have occurred to me to ask if the landlord had failed to pay to run a gas line to the building or was deviating from the traditional NYC methods.

Yes this one does get me...a MS heat pump is a 3 season unit, so what is the winter heat source?

If it's just the MS heat pump than the builder/landlord F'ed up. NYC has about the same climate as we do here in southern Ontario.
I can't see how this would pass code.

I have a small duplex in Ontario. There is a gas wall furnace and electric baseboard in one unit and a central gas furnace only in the other. Both units have separate electric water heaters. As someone said MS heatpumps are really efficient 3 seasons BUT still legal if the heat output is sufficient to keep the place warm (only the efficiency gets awful poor below freezing. Still better than my buildings resistance heaters.
My new tenants in the rear unit owed some past amount to the gas company and refused to pay to hook up the gas in their unit. They chose to heat by electric only
The gas wall furnace had been installed 10 yrs ago because electric heat had become very expensive .Anyway after heating last winter with electric only they added up their bills and realized it cost about $2300 for electricity for the last 6 months. They are now getting the gas connected.
Last winter was one of the coldest on record here.
Your daughters apt will have electric hot water too which is likely accounting for about $4-600 annual of their bills.
If the girls are like my kids ,when they lived at home the house was always lit up like a Halloween pumpkin. Less so when they pay their own bills.
Also consider if the basement under or any other public areas are on the same meter. Landlords should have a separate service for the basement and hallways but small buildings sometimes don,t. Is there in unit laundry or a laundry room Who,s meter runs the laundry.
Too bad these kids didn,t get the big bill at the beginning Then they would have learned to turn off lights and turn down the heat already. I also bet they wash small loads ,like a single pair of jeans, my kids did.

Yes - the fact that it's a new building and with no super, the meters were all behind a locked door and therefore each bill was just an estimate.

It was not super clear, but each statement did say "estimated" usage. And since she's never had an electric bill before it didn't set off any alarms.

Fwiw, the unit is on the second floor, and there is one unit above and one below her.

With a 3 unit total building It,s still possible she is heating a share of the common spaces. Ask her how many meters are on the whole building. Or call con ed and ask them (if behind a locked door you should still be able to find out how many services are connected just not usage amounts for someone else.)
As someone else said ask her neighbours about their electric bills. They should be similar ,if wildly different then either something extra is connected or it all boils down to learning to conserve. There might be only one water heater too. Does her bill from Con Ed include the water and sewage charges too? How much is for a deposit ? Here a new client with no previous history pays something like 2 months average as a deposit (half rebated after a year of good paying
I have seen tenants who would rather open a window in the winter than turn the heat down if I was paying the bill.
Also if her annual electric /water and sewer charges average out to less than $400/3 she is still only personally paying about 125 per month for all utilities which seems a little high but not really terrible for a NYC apartment. My tenants saw a single month bill of $800+ in Feb but are seeing bills of less than $100 now in the spring
Now hope she can operate the apartment for the cooling season efficiently and then see her average for the total year come down.
When you average a very cold winter bill over 12 months it won,t be so bad if the cooling season is normal or even cooler than usual. Remember those mini splits should be extra efficient AC during the summer.