You said something interesting about the problem not being just your job, but everything, every little decision. And that it's not so much depression as overwhelm.
You are dealing with a lot. Relationship breakdown, probable ADHD, perimenopause, challenging job (even though you love it, teaching is hard).
Any one of those on their own can play havoc with your sleep and mood and general equilibrium so no wonder you're finding things so hard.
There was a thread earlier in the week on which several women doing really high-powered jobs were saying how now, during menopause, they were suddenly finding everythng so hard, second guessing every decision, feeling constantly anxious whereas before they'd thrived on the pressure and responsibility, and were doing brilliantly. So don't underestimate how much hormone fluctuations can wreak havoc with your brain.
I honestly thought I was losing my mind and my identity at times.
What I'm trying to say is you're not failing, you're dealing with some really challenging things. It's only to be expected that you're struggling.
It all seems like one big, black fog pressing down on you, and it's making it hard for you to find your way through. You can't see things for what they are because you're overwhelmed. Taking the little steps that would help seems pointless because you're thinking that on their own they won't be enough to help. (I know, I've been there.)
You're also stuck in a spiral of negative self-talk, black and white thinking, catastrophising, ruminating. Feeling ashamed that you're not coping. (Been there, done that too.)
You're really reluctant to go to the gp to review medication, convinced that nothing will work. You say your department will fall apart if you take a step back or time off. You're terrified that you're going to lose your job. You say you're in trouble for crying at work. That you want to self-destruct.
All this is your depression, burnout, out of whack peri hormones etc talking here. It's not objectively true. And with ADHD you've probably spent years masking, using more energy than most people just trying to function "normally" and it's exhausting. (Ditto).
Please, please be kind to yourself, OP.
There are solutions.
You can and will get through this.