Following up on this, in case anyone else has the same issue. Turns out that your NYS 1099-G amount isn't actually supposed to exactly match the NYS refund amount you received. 1099-G amount is calculated (from Form IT-201) as follows:
[line 77, amount overpaid] minus [lines 63-71, various payments and refundable credits] plus [lines 59, 60, and 81, sales/use tax, voluntary contributions, and tax penalty]
When TurboTax shows your refund summary, they (correctly) pull in the 1099-G amount, not your actual refund amount. Would be helpful if they included some language to clarify that.
