If I am a Graduate Assistant at a University and I received a 1099-NEC from the University, what category do I fall under? self-employment, hobby, or W-2 income?

Self-Employment.  This will be reported on Schedule C as self-employment income if it is for income you receive for your services when you are not considered an employee.  This also means you will be subject to SE Tax.  If you did not pay SE Taxes in 2024, and if you plan to do this again in 2025, it may be a good idea to make  quarterly estimated payments to cover your SE taxes of 15.3% and avoid penalties.

To be considered W-2 income, you would have to earn the money as an employee.

Hobby income would be when you are doing something like crafts and sell your products at a market just so you don't have too many in your home.