Question 1 - It depends where the services were performed that resulted in you obtaining the RSUs. If those services were all performed in CA, then you would include the value of the RSUs on your CA non-resident return, pay the tax, and then obtain a credit from NY for having paid tax to CA. If the RSUs that have vested are for services that you performed in NY, then that income would be subject to NY tax but not CA tax.
Question 2 - We need some additional information. The RSUs that you will receive in 2022 and beyond, are those RSUs all based on the services you provided to your company while you were working in CA? If yes, then the RSUs are likely taxable by CA, but you will file a non-resident CA tax return, pay whatever tax is due, and then obtain a credit from NY for having paid tax to CA.
Here is a link to a recent TurboTax article that discusses, in a step by step method, How to enter New York State income as a part-year resident in TurboTax.
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