I was in your situation year ago, three years of agony at a mediocre toxic corporate company where our team was responsible for all the problems but were given no time or resources at all to actually fix the root cause. Only firefighting was allowed.
I was on medical leave, went back, and eventually was offered to quit without serving my notice period (so 4 months paid without working).
It’s been a year since and I didn’t touch a computer for 10 months. I was feeling like shit and really needed the time to recover. I’m still not recovered but much better. I’ve been seeing a therapist to deal with the aftermath for 18 months. It helped. Magic mushrooms and weed also help me putting things in perspective and understanding that it was a failure of that company, not of me.
Burn-out especially when ignored for so long is no joke. I know it feels silly/cowardly/scary to be unemployed, but you really have to get out. Sick leave while still employed at the company doesn’t let you free yourself from all the pain because you’ll have to go back eventually.
I’m lucky that where I live you get employment insurance even if you quit. But if that’s not an option in your country then let them fire you. They created the problem so fuck them. It’s not like you were going to get a good reference from that place anyway.
I would also recommend reading the post on common cog about burnout. It’s well written and instructive.
Bottom line is the longer you stay the worst it’ll get. Only time can heal you (several months, like 12–24) but you’ll get better. It’s just a matter of leaving that toxic place and waiting.
Good luck. It should be criminal to put people in these situations rather than just “cost of doing business” for employers.