No, taking the standard deduction for 2020 year does not apply to the state refunds for other years. What matters is whether you took the standard deduction on your federal tax return for the year that the state refund is for. For example, whether you have to report your 2019 state refund as income depends on whether you took the standard deduction on your 2019 federal tax return. But if you took the standard deduction on your federal tax returns for 2017, 2018, 2019, and 2020, none of the state refunds for those years have to be reported as income. You don't even have to enter any of the state refunds in TurboTax, because they will not appear on your 2021 tax return.
