None of this is new, but such writs are granted very rarely.That's even more unlikely in these cases because if he gets convicted, the sentences would almost certainly be stayed pending appeal, so there would be no need to skip the usual appeals process.
Now, if Trump gets convicted, Merchan sentences him to five years and orders immediate incarceration before appeal, and the New York Court of Appeals upholds that, then you.might have something.
Where you'd definitely have something is if they tried to keep him locked up after he won and was supposed to assume office.