A state tax refund that was paid to you in the Spring of 2022 is taxable income only if you itemized your deductions on your 2021 tax return. That's because you deducted your state income tax withholding, so the refund is a reimbursement of a previous deduction.
A federal income tax refund is never taxable income on your federal return. It may be taxable income on your state return if you live in a state that allows a deduction for federal taxes paid and you received such a deduction, because the refund would again be a partial reimbursement of a past deduction.
