I would definitely ask your school about job offers that will pay you. I understand the mental health exhaustion though, would it be too much to apply for those while you volunteer at the cat café? If so I totally understand and maybe it would be best to focus on one or the other, or do one at a time. A cat café is definitely unique for a resume though, especially in the States.
Do you know if there's a way you could work later in the day? I don't know your class schedules or when the cafe is open but it really helped me going through school to set everything after 11am/12pm even if that meant being in classes/work/meetings until 9pm. Just a suggestion, idk how your college schedules things.
Also, if you're not sure you're ready for a real job volunteering is great! (Sorry, I'm only pushing this so much because I'm excited to see someone wanting to volunteer. I remember hosting events or setting up drives it seemed like no one cared about unless there were consequences for them. So you wanting to volunteer from your heart is amazing)