It will make no difference in your career. It will not overtly add money to your career.
Most job postings for addiction specific are geared more toward community mental health agencies or are part of the large for-profit psych hospital systems and they don't necessarily care or differentiate compared to general psych with pay, or even hiring.
The higher end voluntary inpatient addiction hospitals will pay higher - but they will work you harder - with more patient volume and higher call frequency, and expect that you take those middle of the night admission phone calls. This is because a very tight competitive market for these types of addiction facilities and they don't want to miss the chance to get an admission. You will certainly work for those few extra dollars.
The really high end facilities taps into Sluox-esque descriptions of pedigree and knowing people and well, there are only a few of these doors open and only a few people get to walk thru them. This is also the same for general psych jobs, too.
Private practice, taking insurance, isn't worth it in my opinion. There is such an increase in people doing suboxone, ARNPs, PAs etc and large pseudo-national firms that are suboxone mills that the volume dropped off. I only have 5-10 people in my practice for suboxone. A major need in the community is for medicaid and that typically goes to community mental health agencies or these pseudo-national firms. Alcohol use disorder pops up more frequently for treatment in my office, but this population is notorious for relapse and dropping off the radar. I had toyed around with the notion before I opened up my practice of doing 100% addiction outpatient focus, and so glad I didn't. At times I almost think of not advertising my addiction status any more simply because of the turnover aspect of AUD patients, that time could have been spent focusing on depression/anxiety/OCD which have better follow up rates. If one wants to really make an outpatient addiction practice work, I think you almost have to have the connected IOP/PHP program to go with it, and really work to get the referrals from ED when they discharge folks - but if you aren't taking medicaid, good luck being THE referral for ED Social Workers, and now you are on the same competition level as all the large Big Box shop entities that also offer Residential with their IOP/PHP.
None of my contracts with insurance pay me more for my addiction boards, or any enhanced pay because of it. I get the same generic rates as all the other psych with my insurance contracts.
I was on the verge of applying to a few programs at the end of my residency but reviewing the curriculum and rotations couldn't justify it over simply doing the practice pathway for addiction medicine.