I'm still enrolled in school, but haven't taken a class for 3 consecutive semesters because of an international paid internship. How should I file? As a Student?

There is no such thing as "file as a student".

As to the occupation you enter, it's  not relevant (the IRS uses it for  flagging deductions). I would put "Student Intern".

You (or your parents if you are a dependent) cannot claim a tuition credit or deduction, if you did not attend any classes in  2019.

There is one thing that being a student does affect: whether your parents can claim you as a dependent.  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, relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit .  

Your income is too high to be a standard dependent, so your student status  will determine if you can be a QC. You must have been enrolled as a full time student (FTS) for parts of 5 calendar months.  Does your school still classify you as FTS ? Although in an official job rotation program (e.g. co-op). the student is still considered enrolled; a 3 semester break sounds unofficial (not part of the program).