No, that question in TurboTax is usually to determine if you qualify for an Education Credit, for post-secondary education.
Here's more info on Am I a Full-Time Student?
The IRS definition of a full time student:
Full-time students are children under the age of 19 or adults under the age of 24 who attend an educational program at least five months per calendar year.
The definition may apply to determining dependency as well as education credit as already explained.
Q. Does being enrolled in high school from January - May of 2023 count as being a full time student?
A. Yes. You should select the full time student option.
That question comes up in the personal info section of TurboTax (TT). Your answer is used in determining if you are still eligible to be your parent's dependent, under the Qualifying Child Rules. It is not used in determining eligibility for tuition credits. That comes later, in the program (although checking it in the personal info section will prompt TT to ask about being in school later). The question is usually not relevant for most recent High school grads. It's only meaningful if you are over 18 by December 31.
There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.