Q. Do I have to follow the 3 months rule?
A. Probably. It's clear that the first 3 month rule applies for education credits etc. So, it probably applies to scholarships too. If the Spring term starts in March (even Mar 31), then yes the payment counts as qualified expense for 2022.
Q. Or should I better off considering only Winter 23’s tuition is qualified?
A. You'll be better off counting the Spring 2023 payment in 2022, since that makes it tax free. The real question is "are you allowed to do that". That's not clear. If the school actually bills you (for Spring 2023) in 2022 and you pay it, I think you're on firmer ground than if you just voluntarily pay it in 2022.
