If I cannot claim my son as a dependent but paid tuition, should I report a 1098-T?

No, if he is no longer eligible to be claimed as a dependent, then he would report his own 1098-T.  If he is 24 or over, then he would be fully eligible for the Education credits even though you paid the tuition. 

"If you were under age 24 at the end of 2021 and the conditions listed below apply to you, you cannot claim any part of the American opportunity credit as a refundable credit on your tax return. Instead, you can claim your allowed credit, figured in Part II, only as a nonrefundable credit to reduce your tax. You don't qualify for a refundable American opportunity credit if 1 (a, b, or c), 2, and 3 below apply to you.

1.  You were
   • a. Under age 18 at the end of 2021, or
   • b. Age 18 at the end of 2021 and your earned income (defined later) was less than one-half of your support (defined later), or
   • c. Over age 18 and under age 24 at the end of 2021 and a full-time student (defined later) and your earned income (defined later) was less than one-half of your support (defined later).
2.  At least one of your parents was alive at the end of 2021.
3. You're not filing a joint return for 2021 " Pub 8863 

Edited 3/16/2022 @4:00AM PST  

@kruise 

You cannot claim an education credit for your son's tuition if you do not claim him as a dependent. Your son treats it as if you gave him the money and he paid the tuition himself.

What do your think you can't claim your son as a dependent?