I graduated in April 2021, does that still count as a full-time student?

 In the personal info section, of TurboTax, answer no to the FT student question (you don't meet the 5 month rule).  But,  It depends on why you're asking.  You were a fulltime student for purposes of claiming a tuition credit (but you  only need to be half time or more). 

 

You were not a full time student (the 5 month rule) for purposes of the "qualifying child" dependent rules.  You would have been if you graduated in May, even May 1. 

There are two types of dependents, "Qualifying Children"(QC) and standard ("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.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

To qualify under the qualifying relative rules, you income must be less than $4300.  

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html

High school or college?