When I was in college there I picked up a part time job teaching English at GABA, and while it was manageable I did have some rough days where I was definitely sleep deprived, and even got yelled at for falling asleep in one class. I think if it's something simple and you have a loose schedule with short shifts it shouldn't interfere with your studies too much (gaba was nice because I could set my own schedule, but I did have to wear a suit), just know your limits and don't burn yourself out. A part time job like at a convenience store or something could be a fun way to practice Japanese in your spare time
Being on a student visa, I needed to go to the immigration office once or twice to get a special stamp on my visa to allow me to work part time (I think 14 hours/week was the max allowed). It was nearly 20 years ago now, but I don't have reason to think the rules have changed that much.