Simple answer: Yes, you report the $2021 as taxable income. The simple way to do that is: at the 1098-T screen, in TurboTax enter $2021 in box 5 and 0 in box 1 (the 1098-T is only an informational document; the actual numbers on it are not required to be entered onto your tax return). If you paid for books or other required course materials, with any of the $2021, reduce the amount you enter, in box 5, by the amount you paid.
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But, there is a tax “loophole” available. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.
Using your numbers: Student has $5969 in box 5 of the 1098-T and $3693 in box 1. At first glance he/she has $2276 (or $2021) of taxable income and nobody can claim the American opportunity credit. But if he reports $5969 as income on hi return, the parents can claim $3693 of qualified expenses on their return. This will get them somewhere between $969 and $2423 depending on their tax liability; which is a lot more than the little extra tax you will pay.
