Absentee ballot not arrived

[cmh]

I am an NYC resident who requested an absentee ballot early last week with the "covid" reason that allows anyone to vote by mail here. Haven't received it yet and am wondering 1) by when should I expect it to arrive, 2) if it hasn't arrived by election day, can I still vote in-person and would that in-person vote still count, and if yes then what should I do with the mail-in ballot if/when it arrives?

[cmh]

I was told it's because I'm not registered to a political party so I'm only eligible to vote in the general election in November (didn't realize the current election is party-specific).