No, a Form 1099-G is issued by your state to report the unemployment compensation received or a state tax refund received.
The stimulus payments are from the US Federal Government through the Treasury Department and IRS. You would have received a Notice 1444 in the mail for the stimulus payment.
The stimulus questions are asked in the Federal Review section of the TurboTax program. Any payment you were eligible to receive based on the 2020 Federal tax return but did not receive will be entered on the Federal tax return, Form 1040 Line 30 as a tax credit. The credit is included in the federal tax refund or it will reduce the amount of federal taxes owed.
