The test is not whether "your earned income is greater than half of your support"; it's whether more than half your support comes from your earned income. But, that is probably academic since your are only claiming the non refundable AOTC and you already said "There is no question that I do not actually provide half of my own support for the year 2024." The support from earned income issue only applies to eligibility for the refundable portion of the AOTC*.
As a student-dependent, away from home, for school, you are only considered as temporality away from home. As such, the support value of that home counts as support for the whole year, not just the time you are actually there. The support value of the home, provided by the parent, is the fair market rental value of the home plus utilities divided by the number of occupants, including the student.
Money the student puts into savings and investments does not count as support he spent on himself.
The treatment of expenses paid with distributions from Sec. 529 plans and Coverdell ESAs in the support test is uncertain because of the dual nature of these college savings vehicles and a lack of IRS guidance. The consensus among tax experts is that it is parental support, because the parent is the owner of the plan.
* A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) 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.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable).
