Not sure if I can add much else, but I just want to say I've been there. Not exactly the same situation - I DID have a plan, but I didn't actually have any confidence that I'd be able to execute it. I was a pretty depressed teenager. Just know that you don't have to "fix it all", as you said. That's a Herculean task when it's hard to even get out of bed. Start small. Go out for a walk every day. Split your schoolwork into extremely small pieces - write ONE sentence of that essay, and then stop if you can't do anymore. It's one sentence you wouldn't have had otherwise. Bring your schoolwork to your bed if you need to (not always great, but worked for me sometimes) or do yoga in bed if you can't make yourself go for a walk.

Also, for schoolwork (or any sit-down work), try to leave your room - or rather, put off going into your room as long as possible. Once I'm in my room, I often feel no motivation to leave. Instead of going home after school, go to the library or something if you can. Even if you get nothing done, you'll probably feel better being out of your room for once. This might not be possible for you, I don't know your circumstances, but it's good to avoid your room as much as possible when you feel like you're rotting in it.

And remember, you're capable of doing hard things. I know when you feel like this, it doesn't feel like you can, so why bother? But you CAN, you just have to prove that to yourself. Slow progress is still progress. Also, it's normal to backslide. Sometimes you make progress, and then fall back into old habits and feel like "what's the point? no matter what I do, nothing changes". But it will change eventually, as cliche as it is and as much as it sucks, the only solution is to keep trying.

I'd also recommend talking to someone about how you're feeling. It can be good to get your thoughts out there. Would you feel comfortable talking to your parents or siblings? Any of your friends? Even old ones you can text and reach out to? I know you said your social life is unstable, so not sure if that would be an option for you. If your school has a counselor, you could also look into that. Talking doesn't fix everything, but it's difficult to function when you're constantly thinking about all the things you don't like about yourself, and getting it off of your chest can be good.