It does depend on the state, and in some there's even no permit, but in most that have them they do instruct about basic safety and use of force laws. That is however relegated to the state to form their own policy, and changes all the time. If you feel your state should do more it's easier to work on that then federal, so it's probably more effective this way tbh.

Honestly there isn't much to gun safety, either, it isn't actually all that hard and doesn't really take too long to learn. The hard part is making sure people adhere to it at all times, which tbh is functionally impossible beyond "if you see someone being unsafe, say something" which is common to do amongst gun owners, but doesn't prevent everything. Accidents can happen at any experience level, it's also a common saying amongst experienced gun handlers/owners that "complacency kills," and it does, it's something you have to be ever thoughtful of while handling one (not always while carrying, I mean, but while it is out of the holster for any reason. Be it defense, range unloading/cleaning, leaving it in the car because of a no gun sign, etc.)

Also, just as a sidenote, something you can test for yourself: Go to any pro gun forum, say r/firearms or whatever, or c/leftistgunowners here, any one, and make a post saying something along the lines of "Hey I've decided it's time to pick up my first gun, any advice?" I guarantee you many posts will say "welcome to the club," many more will say "buy you a glock" and almost all of them will say "but it isn't enough just to get it and put it under your bed, learn how to be safe and learn how to use it at the range. Last thing you want is to kill someone innocent or die fumbling with it because you never learned how." It isn't a legal requirement, and of course you could just waltz into a gunshop and avoid most of that, though they will also offer advice most often if they know it's your first, but at least the culture at large generally is pretty safety conscious already without it being mandated, so at least that's something.