Employer-Provided Assistance timing issue between paying and reimbursed / taxable income in w-2

Help  please! Trying to confirm if I should amend last year's taxes. I didn't enter 1098-t because I got tuition reimbursement by employer. However, I have now realized that the amount above $5,250 was getting reported as income on my W-2, so I should enter 1098-t because I will get a credit for the amount of total tuition paid less $5,250, right?

 

To make it more complicated, I am trying to do it right this year, but because of the delay between paying in tuition and getting reimbursed (I get reimbursed once class is over, sometimes in new tax year), I am getting reimbursed by more than I paid. I was reimbursed $9k in 2022, but my 1098-t only shows $6k. I got $5,250 tax free, and the remaining ~$4k is getting reported as w-2 income. So I am getting a very small education credit due to 1098-t saying I paid $6k but having to enter that employer gave me the $5,250 tax free in the section that asks "Enter the amount Sean received. Don't include amounts already listed on a W-2 or other tax form.".

 

I am thinking what will fix it is if I amend 2021 to add the 1098-t, I can show that I paid $9k in 2021, was reimbursed only $6k, of which $5,250 was tax-free but the rest was on my w-2 wages. So essentially for 2021, I would get a tax credit for the fact that I paid a lot more than I was reimbursed for (in that year).

 

Is this correct? Thanks in advance!