Gosh, first off welcome. And I applaud you for your courage and the love you must feel for your son to come on here.
Allot of us were very much like your son. Not necessarily bed-wetters, but we were so much happier in diapers.
I am 61 now, and never wanted out of them. I knew about this side of myself when I was 4 years old, and in some form or another put myself back into diapers. Back in the 60's and 70's this was perplexing to me as you can imagine. I was all boy, but just very happy when I was in diapers. Now, ask any 60-70's mommy about their son wanting to be diapered and they would go through the roof. There was nothing to explain it. And I felt like I was the only person in the world. I could not talk about it, I could not share it... it was scary and lonely. When I married, I was so afraid of my wife finding out and loosing her, I literally gave them up for 30 years. 30 years later as my life took a turn for the worse, I told my wife about this. It was the scariest moment of my life. I had held that secret for over 50 years. She fully embraced this side of me. IT WAS LIKE 10,000 pounds coming off of my shoulders. I am diapered more often than not now, and I am a much happier person.
Most people here that have known about this side of themselves since they have been little, will tell you that when they are diapered they are much more relaxed and happier. If they can share this with their significant other, all the better as it removes allot of the stigma and shame that surrounds this, especially for a male.
You say that your son is happier and more relaxed and that is fantastic. Additionally he does not have to live in constant fear about mom or dad finding out. You can also help to shepherd him through this. I am guessing that you have already consulted a physician regarding his wetting to eliminate any physiological causes? I wont tell you to take him to a shrink or therapist although you have probably considered that. Many of us on here have tried to give up this urge, this incredible draw. As I said I literally did it for 30 years, but it was always there with me. Many have tried therapy to no avail. If your son is a true diaper lover, it can be for 1000 different reasons. None of us have really figured it out. We all have some idea what the initial trigger was, but I dont think that anyone knows for sure.
There are a few books out there regarding teen diaper attraction written for parents:
https://www.goodreads.com/book/show/42368256-so-your-teenager-is-wearing-diapers
I am sure there are more... if you search around.
Bottom line, keep the lines off communication open with your son. Help him to find appropriate rules for wearing. DO NOT let him tell any of his friends no matter how understanding he thinks they might be. At that age a friend today is not one tomorrow, and this information is damaging in the wrong hands. As I said, I held this secret for over 50 years and over 30 years from my wife. Let him know that no matter what you still love him.
A therapist once told me, "of all the things that I could have gotten involved in to control my stress, drugs, alcohol, sex, pornography, this is nothing!" It is not illegal or immoral, it is just an odd choice of underwear for an adult. But I am a much much happier adult now. I really wish that I could have shared this with someone years ago... perhaps even my mother, but she would have come unglued and I would have ended up in an institution.
Long term damage. I doubt it. Most of us have this in balance and it does not overwhelm our world. Many of us are married, have families, have higher education 6 figure and better careers. Your son has one thing almost all of us did not have, a mother who is trying to understand, loves him, and help... good for you.
We are here for you.