Colleges work in academic years, the IRS works in calendar years. So the reality is, it takes you five calendar years to get that four year degree. With that said:
Qualified education expenses are claimed/deducted in the tax year they are paid. It does not matter what year is paid "for".
When you dropped the check in the mail or handed it over to the payee, on that date you lost control of that money. I call that "constructive receipt" of payment by the recipient. That date is the date you paid it. Doesn't matter when they cashed the check.
I would expect you to have a receipt of some sort to prove they received/accepted the payment in 2021. That's all you would need if you were ever audited on it.
