The language from the New York Dept. of Revenue is somewhat ambiguous, but if you are required to file a New York return (New York source income), separate returns are the way to go.
The 2020 Instructions for New York Form IT-201 Full-Year Resident Income Tax Return page 6:
Separate returns are required for some married taxpayers who file a joint federal return. If one of you was a New York State resident and the other was a nonresident or part‑year resident, you must each file a separate New York return. The resident must use Form IT‑201. The nonresident or part‑year resident, if required to file a New York State return, must use Form IT‑203. However, if you both choose to file a joint New York State return, use Form IT‑201.
For your reference: 2020 Instructions for New York Form IT-203 Nonresident and Part-Year Resident Income Tax Return"
You could try filing a Joint New York return to se if the part-year resident income is allocated correctly. If it is broken out on W-2's as such, it may not be a problem.
Otherwise, you would need to prepare a 'dummy' separate Federal return (in another online account) for each of you to have the info flow into separate New York returns properly, or use the TurboTax desktop product.
Click this link for more info on Married Filing Separate State Returns.
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