No, the 1099-NEC (Non-Employee Compensation) can only be reported as Self-employment income.
The main reason is that the internship does not go through the hassle of establishing you as an employee, so does not pay your FICA (Social Security) tax.
Your "Self-Employment tax" is the FICA tax you would have had withheld had you been paid as an employee.
You do pay both halves (Employer and Employee) but you get a credit for half, so it ends up the same as if you were paid with a W-2.
Shouldn’t they have filed a 1099MISC instead of a 1099NEC since I am a student who was interning during the summer and received a stipend through the program?
You may wish to contact the program that sent Form 1099-NEC to confirm they intended for this to be earned income rather than an honorarium. Generally, a 1099-NEC is meant to report services from someone who is not an employee (an independent contractor) and is subject to self-employment taxes.