I returned to a previous internship while studying full-time in university for one semester. My class schedule was around 40 hours/week, studying and completing assignments took up another 30-40 hours, and I worked 10-15 hours. I also took up some extracurriculars, which probably took up 5 hours at most. I made sure to communicate my academic obligations to my manager, and they were understanding of the rigour of my program. The context is different, though time management is key in both situations.
Block out time in a calendar (digitally or on paper). Hopefully, you know your work hours at both your gigs ahead of time. Mark off times when you have a shift, block off times for basic life activities (sleep, shower, eat), and finally fit in other activities (errands, social events, personal time, etc.) around your shifts, like time tetris. For sleep specifically, I had an absolute minimum sleep schedule (midnight to 7 AM) and a nice-to-have schedule (11 PM to 7 AM), though I normally stuck to the minimum since I prefer the predictability and routine.
Know your limits. I have a hard time saying no to commitments I had originally thought I would have capacity/energy for. Looking back, this semester was the one where I felt exhausted all the time and miserable. It didn't help at all that I had very little time to socialize.
Minimize the number of decisions you have to make each day. Making decisions take cognitive load, and you probably want to save that mental capacity for the things that really matter. For example, something I did was keep a spreadsheet of recipes I enjoyed, deciding on what food I was in the mood for, then getting groceries and doing bulk meal prep on the weekend. I also laid out my clothes for the next day before I went to bed.