"how much of the $1k is taxable?"

You confused Taxable and Reportable. You Report it, because itemization means things were reported to attempt to benefit from them. Since it was reported and resulted in a refund, the return of what was reported in the previous year is included in the year of the refund, to see how it affects that tax return.

If you were not itemizing, you would not be detailing taxes paid, to benefit from them as expense. That's why it is added back, later, if any of it is refunded. That won't make it taxable. It's just another piece of the puzzle.