It goes in Box 3, just like on your 1099 (Not Box 6). Examples given of Box 3 "other income" include cash (which you essentially received) or a check from the Alaska Permanent Fund.
If you are using TT in interview mode, when asked by TT to describe the reason, just put "California Middle Class Tax Refund." And then on the next screen, "None of these apply" for uncommon situations. On the following screens, choose:
-- its not related to your main job
-- you got it in 2022
-- it didn't involve an intent to earn money
This will place the income on line 8z of Schedule 1, and transfer it to Line 8 of the 1040 (Other income). You can then adjust it off for the California return on Schedule CA under "Subtractions". That way it isn't taxable for the State, just Federal.
Note that the IRS hasn't made an tax exception for any funds that States have distributed in this manner. People who got less than $600 did not receive a 1099 from the Franchise Tax Board, so technically they also owe tax, but they can probably get away with not reporting it.
