My daughter had a similar summer experience after her first year of college. She applied to 20+ jobs. Eventually, she took a job as a camp counselor which paid $2.50 an hour, quit that after three weeks, and got babysitting jobs the rest of the summer.
We realized in hindsight that she had mostly applied to jobs where they needed part time workers, but not part time workers who would leave after a few months and return to college. They don’t want to invest the time training someone who is going to leave soon. I suspect that could be a similar thing here. Your son would only be able to work outside of school hours in the fall, so maybe it’s not worth it to employers.
Here’s the thread I posted back in 2017. Interesting responses. Why can't my daughter find a job???