I assume you paid for the winter 2022 room and board in 2021. This means that room and board, alone, fully covered the 1099-Q ($10,000 > $6864). The 1099-Q does not need to be entered on either your return or the student's tax returns.
You have $13,772 + 800 = $14, 572 of QHEE*. Use $4000 to claim The American Opportunity Credit, That leaves 10,572 for the scholarship. $11,000 - 10572 = $428 of taxable scholarship to be reported on the student's tax return.
Since $2709 ( $2281 + 428 ) is less than the $12,550 filing requirement, he is not required to file a tax return, unless he needs to get a refund of federal withholding (box 2 of the W-2)
*QHEE - Qualified Higher Educational expenses
