How should we report fellowship income that is more like a stipend without duty?

I have a question regarding the classification of a Ph.D. Dissertation Fellowship for tax purposes. Specifically, I am unsure whether this type of fellowship should be classified as income (on somewhere we don't know) or reported as "Other Scholarships/Grants/Fellowships" when filling out my tax return.

 

To provide some context, my spouse received a Ph.D. Dissertation Fellowship from her university's graduate college program for the academic year 2022-2023. This fellowship is not for paying school fees, as she is a graduate student and the university does not ask her to pay tuition, although she still needs to pay other fees. The fellowship is actually more than a stipend without any duty. The reason we ask this question is because we realized how it is reported matter a lot for us: we ran an experiment by reporting the fellowship as income on the W-2, which will enable us to claim the American Opportunity Credit. However, when we reported it as "Other Scholarships/Grants/Fellowships," we were not eligible for the credit. The key difference is that the scholarship amount exceeded the allowable school expenses. Then we started to find that in the explaination of "other scholarship", it says: 

 

"A scholarship or grant is generally money that pays for a student's undergraduate or graduate education.

Enter scholarships and grants that were used to pay for tuition, fees, books, supplies, and equipment, and the student was required to pay the institution for these expenses."

 

That puzzles us because the fellowship is to support my spouse living when she works on dissertation so we wonder whether we should report it somewhere else.