why I should pay tax on state CA refund

@vijay-saikrishna  TurboTax is asking the questions  ( like whether you used  standard deduction or  itemized deduction ) to compute  if  and how much of the State refund  should be taxed.  This has been around for  ages.  If you used  standard deduction then none of the refund is taxable for federal purposes.  If you used itemized deduction then it uses  "sales tax " for your AGI   or the actual  SALT you sued  to see how much of the refund should be taxable.  e.g. if you used  State tax of 8000 for your federal return in 2023 and now got back  1000 as State refund then  TurboTax will compute both ways  ( SALT and Sales Tax choices )  for  taxation of the refund.  That is the theory behind this --- 

Is there more I can do for you ?

If all three of the following are true, your refund counts as taxable income(may not be the entire amount):

• You itemized deductions last year, instead of taking the standard deduction.
• You claimed state and local income taxes (not general sales taxes).
• Claiming the deduction helped you increase your federal refund or lower your tax bill.

TurboTax will calculate the taxable amount when you answer the questions about last year's refund. 

Does this matter, which year the state refund belongs to? 

For example, due to amendments if I received $2000 (for 2022 tax year) in 2024. 

The reason I am asking is that since I got refund from a previous year, do I need to file an amendment for 2023.

The refund would be included on the tax return for the year that you received it. So if you got the 2022 refund in 2024, it would be reported on your 2024 return. No need to file an amended 2023 return.