Yes, you have it correct.
Q. Does that part need to happen when she starts doing her taxes with TT next year for 2022?
A. No. It's all done on the 2021 return in the 2021 software. It can be done anytime before you start your 2022 tax return, in 2023, by transferring the 2021 data. I would go ahead and do it now while it's fresh in your mind.
Q. Are the previous year's W-2 and income amounts even mentioned on the next year's state return?
A. No. For most people, the changes are probably not needed for your 2022 return. But it's best to have it updated. One item that sometimes makes a difference is the amount of your refund or the amount due*. But, you're given a chance to verify/correct those items in the 2022 program. The W-2 info (employer name and EIN etc) transfer to next year's return, but no amounts.
*The amount of state tax paid, during the year, is deductible on the federal return, if you itemize deductions. The state tax refund MAY be taxable, on the federal return, if you itemize
