Each count says "[the orange thing] . . . with intent to defraud and intent
to commit another crime and aid and conceal the commission thereof, made and caused a false entry . . ." Unless I'm missing something, it doesn't specify the "another crime."
Here's what Bragg reportedly said:
>>>Manhattan District Attorney Alvin Bragg said at a news conference after the court hearing that the alleged scheme
was intended to cover up violations of New York election law, which makes it a crime to conspire to illegally promote a candidate. Bragg also said the $130,000 payment exceeded the federal campaign contribution cap.<<< (emphasis added)
There has been a lot of speculation as to whether or not the New York law is limited to intent to commit another crime under New York law or if the additional crime can be based on a federal law.
Depending on how closely we want to parse the statement by Bragg (which is not in quotes, so it's not clear exactly what he said), he seems to suggest they are planning to argue that the false entries were made with the intent to commit crimes under New York election law.
Although he says the amount exceeded the federal campaign cap, he didn't say the false entries were intended to cover up violation of the federal cap.
I doubt that the statement attributed to Bragg can be taken as a definitive statement of the DA's theory of the case.
I'm sure we'll hear plenty more in the near future.