New York State has different nomenclature than other states. It is not "weird" because in other states Merchan would have a title that matched the nomenclature used there. In my state he would be a District Court Judge. You should not let such a minor matter throw you. In New York State the "Court of Appeals" would be the equivalent of my states "State Supreme Court". Just different terms for the same jobs.
Yes, I know that. It's one of the many oddities that is unique about the legal system in New York. It's not that it threw me so much as the fact that most people outside of New York don't know that the "Court of Appeals" corresponds to the "Supreme Court" in most other states. Calling the Court of Appeals an "appellate court" therefore leaves people outside of New York with the impression that Trump can further delay proceedings with an appeal to the New York State Supreme Court.
Trump could still try to get his friends on the Supreme Court to help him, and I think they would jump at a chance to do that. So they will probably try to use some excuse to get it up there, just like they did manage to get the goofy "absolute immunity of Presidents" defense. That effectively sidelined Trump's criminal trial for federal election interference, because the Supreme Court has sat on a decision for so long that it will likely have to wait until after the election.
I'm not sure that Trump will need to do an end run around New York state via the Supreme Court, because he may not get any prison time at all for the felonies he was convicted of. My guess is that he is likely to get probation and some other restrictions or fines. So, if he wins, he will break another record--the first serving US president who is a convicted felon.