My approach would be a bit different. If indeed you neither lived in nor worked in CA in 2022, I would go ahead and file a non-resident CA return showing zero CA income for that year. That would be a valid return and would reflect the actual situation.
If (and only if) your return is questioned by the CA FTB, I would respond with your own explanation and a copy of your 2022 full-year resident NY tax return. IMO that would be the most acceptable proof that you were a full-year NY resident in 2022. Letters from an employer can be hard to come by.
Your situation isn't that unusual. Employers make withholding mistakes all the time when their employees move from one state to another.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
