I get where you're coming from with needing an official diagnosis for work accommodations, but none of your friends are really going to demand to see a doctor's note, so why would personal relationships depend on an official diagnosis?

The same reasons as from a professional experience. Yes they aren't going to pull the doctor's note but neither is work IMHO. What it does is provide more weight behind your words of "hey I'm not just googling this shit. I'm not just an insufferable asshole looking to validate that I am. I'm actually working with a psychologist."

Friends, just like coworkers, etc. care less of the diagnosis. They want to know you're working on you because I'd argue writ large people want to see you succeed. A self-diagnosis can help but it doesn't give you access to all the tools you may need to succeed so from the outside I would argue that official diagnosis matters. It means you now have someone else on your "team" be it a GP or a psychologist or whatever helping you navigate things.