I regret to inform you that, in many places, there aren't even licensing bodies to regulate who can become a therapist. Even when there are, you usually need a psych undergrad (or something you can vaguely claim is equivalent) and then like a year or so of postgraduate study; it's unusual for therapists to have a doctorate unless they're some kind of half-retired psych academic who wants an easy job listening to sad rich people whine. It's tragically extremely easy to become a therapist if you're a moron.
Clinical psychiatrists do require a doctorate, but in many places, literally anybody can set up shop as a therapist.
"Stimming" is short for "self-stimulatory behaviour"; it does in fact refer to performing repetitive motions, alongside a range of other self-soothing behaviours, and it's not unique to autism (some behaviours regular people do, like drumming fingers or playing with their hair, technically falls under self-stimulatory behaviour), though you're correct in that dipshits on tiktok like to do stupid fucking dances and pretend that's 'stimming' as opposed to attention whoring. It's commonly used even in
academic literature, and if you're a therapist then you should either know the term, or should realise instantly what it's referring to with minimal explanation. If Wedge's therapist needed extensive education on this, then either the therapist is a retard, Wedge is using a retarded definition for it, or Wedge is lying.
"Overstimmed" is a stupid way of saying overstimulated. Autistic people of all "levels" of autism, including very high-functioning ones, can get overstimulated; even regular-passing autistic people can have shutdowns (i.e. they stop functioning as a human) or meltdowns (i.e. looks like a temper tantrum). Again, people who are non-autistic can get these, too - usually people with ADHD/other brain issues, or kids, but even regular people. Again, unless the therapist is a retard or Wedge is using a dumb definition, the therapist should really know what "overstimulated" means or looks like.
Spoon Theory is actually generally well-known by therapists ime, and can in some circumstances be very useful to describe the difference between "tired because I didn't get enough sleep" and "tired because I have depression and it's sucking my soul and ability to force myself to do stuff into a black hole"; as with every useful psych / mental health / abuse term, however, the internet has done its best to grind it into meaningless dust.
Alters are a load of heaping internet crap though. Even in "proper" DID, they're kind of up for debate.