Student status accidently unchecked on 2023 taxes

That question appears when you enter the education section in TurboTax and it also appears when you enter the Form 1098-T. As long as you answered it correct one of those times you should be OK. You can prepare the amended return just to be safe though and if your tax doesn't change, you don't need to file it.

The only place, on the actual IRS forms, for a box for half time or more student is on form 8863, on which you claim an education credit. 

If the box is unchecked, you will be disqualified from the more generous American Opportunity Credit (AOC). You will be allowed the Lifetime Learning Credit (LLC). 

How much education credit did you get (Lines 8 and 19 of form 8863) and  home much qualified expenses did you enter (lines 1 & 10).  If you got what you were suppose to get, you should not need to amend. 

You appear to be talking about your student's tax return, not yours.  Be advised that a full time, unmarried, student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOC) if he/she supports himself by working. She cannot be supporting herself on student loans & grants and 529 plans and parental support.  It is usually best if the parent claims that credit.