check out past threads, this has been discussed before in useful ways.
I did a psych fellowship and mostly work in a general psych private practice now + some addiction work at an unrelated facility. I do really enjoy working in addiction and hope to change the balance of things in the future. That being said, I probably would not do the fellowship again if I could go back. It was a fine training program, but my original goals (academia) changed significantly when I had a kid and non-career stuff became a priority. To answer your questions:
1. No, particularly if you can get some experience in your regular resident rotations or via electives in your fourth year. Apart from training, you'll learn a lot by actually working in addiction after you graduate from residency regardless of fellowship training.
2. No. It's not going to be financially worth it unless you are building some super specialized cash private practice. There's perhaps an argument to be made it'll be easier to rise within certain organizational hierarchies if you have specialized experience, but I don't think fellowship training is the limiting factor here (more like your particular personality, leadership style etc.).
3. Anecdotally during my job hunt, I saw many detox/rehabs are posting jobs w/ a preference for a fellowship (addiction med or psych) trained physician. In reality when you talk to people, I think most places are just looking for someone who is comfortable doing the work, has a pulse, unrestricted license etc.
4. Other than screening for common medical comboridities of particular routes of substance use (e.g hepatitis in someone who injects), I don't do do much traditional "medicine" and have no desire to do so. It's not something I'm being asked to do, either. I don't want to manage someone's abscess or hepatitis. If someone is in DTs... I send them to the hospital. Unless you work in an inpatient high acuity detox (e.g w/ phenobarbital drips) or ICU, you're not going to be actively managing DTs as a psychiatrist in the vast vast majority of settings (and you shouldn't be).
-therapy training will be critically useful to you as you help people work through ambivalence about their use, all of the social ramifications of problematic substance use, existential concerns as people emerge from using substances etc. I would not downplay this, this are useful day to day skills.
The best use case for an addiction fellowship is if you want to do something in academia (particularly research). Perhaps it would open up other opportunities in tech/telehealth companies, public policy roles etc. but these specialized opportunities do not materialize just because of your training, rather years of working in the field, networking, history of leadership etc.
