Hello~This should be stopped as soon as possible. The battery might leak and then get into his system. It sounds to me like this is due to some form of stress. You said he is extremely active, I would try to find some ways to channel that.
If this chewing on items continues, I think it may be necessary to take him to his pediatrician.
So, chewing is a sign of some anxiety in kids. We often are inclined to soothe ourselves and oral soothing in the form of chewing is quite common in children. Would you describe your child as anxious? Think of things like pacifiers for babies. Soothes them, right? That continues. Adults might chew gum or smoke. This is oral soothing. What can you do instead? That's key. My son chewed on his shirt sleeve or collar. All the time. Or the strings in a hoodie or on his backpack. I gave him some gum, I got him a rubber P that he could hold and chew on. They make things that go on the back of pencils for kids who chew. They make beads they can chew on. Sensory shops online have many items designed for this purpose. Helping a child have better coping skills is the most important part. Why is your child anxious? Are there triggers? Is it showing in other ways too?
Batteries are dangerous. That needs to be something that a firm rule is made about. NO chewing on batteries. Many kids can be black and white and they will adhere to a rule like that. good luck
How old is your child, by the way? Things to also look into are adhd or sensory integration disorder.