Deaths will definitely lag, but new hospitalizations should drop very significantly.
Add the shenanagins that Cuomo played and the real number of NH deaths is much higher.
According to that NYT link, there were over 1.1 million cases in NHs, and according to your tweet there are currently 1.3 million NH residents. It sounds like nearly every NH resident around the country already got COVID.
1.1m is over a year, 1.3m is current. I don't know if my tweet is accurate or not, but it's possible there were twice as many residents over the year or more, I'm sure there is some turnover and many left or died.
Also, the 75% means first dose, no? Israelis are already administering the 2nd dose.
They're not up to the second dose yet for NHs, that should be next week. But a week or two here or there isn't critical, the US government has checks and balances, it can't operate like the souk Israel is