The relevant NY law originally said that
"Written instrument" means any instrument or article, including
computer data or a computer program, containing written or
printed matter or the equivalent thereof, used for the purpose
of reciting, embodying, conveying or recording information, or
constituting a symbol or evidence of value, right, privilege
or identification, which is capable of being used to the advantage
or disadvantage of some person.
The modification adds:
For the purposes of this article, a card provided to a person by a
vaccine provider indicating the date a person received a vaccination
against COVID-19, the type of vaccine and its lot number, and bearing
a government logo or other indication that it is created by a
governmental instrumentality, shall be considered a written
instrument.
This is an unnecessary modification: a covid card is plainly a "written instrument". Working through the definitions of falsely made, completed or altered, we see that a covid card modified as described is a forged document, and always has been one. Actually using a forged instrument is a crime, and has been so, and even possessing one is as long as you possess or utter it "with knowledge that it is forged and with intent to defraud, deceive or injure another".
So, (1) it is a crime in New York, (2) it has long been a crime in NY and (3) is probably a crime in other states, when there forgery laws are functionally equivalent to NY laws. For example, in Washington, RCW 9a.60.020
(1) A person is guilty of forgery if, with intent to injure or
defraud: (a) He or she falsely makes, completes, or alters a written
instrument or; (b) He or she possesses, utters, offers, disposes of,
or puts off as true a written instrument which he or she knows to be
forged.
It does not matter if you forge a document in a state where it is legal (if any such state exists) and then transport it to a state where forged documents are illegal. If you possess it and intend to use it knowing that it is forged, it is a crime.