How do I permanently disable Personal Hotspot on my son's iPhone?

Contact your cellular carrier again and ask them to remove that feature from his line. They should be able to do that for a single line on the plan without affecting the others. If they say they can't, escalate the call.

If it turns out they won't (there is a difference between won't and can't) I'd seriously consider switching carriers. That or take the iPhone away from your son and give him a dumb phone with no data service at all.

I tried disabling changing Settings/Cellular to Don’t Allow in Screen Time settings, but it doesn’t disable Personal Hotspot.

Other than telling him there will be consequences if he uses it when he shouldn’t, there isn’t much you can do. Technology can be an aid to parenting, but not a replacement for it.

Making that feature controllable is a good idea; the best place to suggest something to Apple is here→Product Feedback - Apple

This has been an ongoing problem since at least 2023 if not beyond. For example, see this post.

I know people who have submitted the feedback to Apple but for whatever reason, Apple has still not addressed this gap to allow us to manage our child's devices.

Have you contacted the school's IT people? If the laptop is school-issued, they may have ways to restrict what networks he can connect it to.

@laugher: That’s where parenting comes into play.