Q. My employer doesn't think I can get paid again this year. Is this correct?
A. Yes. You're limited to $5250, tax free reimbursement payments, per calendar year.
You're employer has options. They can pay you in 2021, but it will have to be considered taxable income (meaning both you and they will have to pay your/their share of FICA too). They can wait and pay you in 2022. The payments do not have to be made in the same year as the education nor match your payments to the school.