I'd get really icy over someone doing this to me.

At best it comes from a place of good intentions but there's a fair chance that it comes from a different place as well. As your chronic auDHD burnout buddy, I can assure you that I've had people pull similar shit on me because they either want their free resource to start working consistently again or they feel latent discomfort/helplessness about being confronted by my own circumstances and, instead of owning that and dealing with their own emotional reaction to it, they project it out onto me and demand that I start doing x and y so they don't have to experience that discomfort or helplessness anymore. Which is really selfish, although not uncommon, and I'm going to liken it to when someone misgenders a trans person and makes a big production out of apologizing which, ironically, creates a whole lot of additional emotional labor for the aggrieved party - if you misgender someone then the last thing you should be doing is centering your own discomfort and essentially forcing forgiveness out of the person you misgendered; don't go putting more on someone else's plate while you convince yourself that you're doing the right thing and that you're helping them. That's a very self-centered attitude.

I think I'd tell them that I don't take kindly to the presumption that I'm not already doing everything that I can, that they know my circumstances better than I do, and that although I'm not opposed to them talking to their therapist about me if it's about navigating their own stuff like emotions, boundaries, and our friendship, I am very disappointed that they are conveying what they assume are my symptoms to their therapist on my behalf without my consent (which is tantamount to gossip) and that I'm even more disappointed that their therapist saw fit to diagnose me in absentia, that this was very poorly handled by their therapist, and it feels like a violation of their professional ethics.

This would likely burn a bridge but, honestly, I don't have the time or the energy for that shit (see above re: chronic burnout) so if that's gonna burn that bridge then I take a "so be it" position. A therapist should know much better than to dive headlong into triangulation and to be so careless about it, even if that's not what is going on here (not that they have the ability to know the truth of it). It's extremely reckless of them.

Caveat to say that, clearly, I'm bringing in a ton of my own emotional baggage into this discussion right now and that's coloring my response to it so take what I've said with a good pinch of salt and maybe run it by someone else who is trustworthy and has good emotional awareness before you go agreeing with what I've said here because I'm very much in my feelings on this topic.

My dark humor is that I find it odd society is so against nonverbal autism - when what they really despise is actually listening to people on the spectrum. I hear you. I’m pretty impatient (read overly forgiving) of this sort of thing and give one or two chances to improve before you’re dead to me. Also fuck their garbage-ass therapist lol

Therapists make comments like that all the time. More (maybe most) of them need training in patholigization and how and why its harmful. Ive dealt with therapists saying to me "oh damn that behavior is not ok! Sounds like shes bpd or something", and like i can totally see someone who wants to "fix" you latching on to comments like that and substituting them for an actual diagnosis. Not to mention even shittier therapists who actually try to dx someone based entirely off another persons reporting of them.

As far as countering the accusations, you could go the vulnerability route, and level with them and explain adhd, autism, and your direct experience of autistic burnout, laying out how it affects you and what you do to mitigate it. You could also try telling them that the way they approached you came off as aggressive? Idk, tbh when people have done this stuff to me theyve either been like 18 and literally dont know what theyre talking about, or older and its kinda been the lifting of the veil that makes me distance myself from them.