Honestly, she sounds depressed. People who have lack of motivation to clean up or do certain things that should be normal to doing so on your own, are depressed.
You should break up with her, she doesn't deserve to be treated like that by you. Giving her an ultimatum because she's severely depressed and you cant take the time to notice she needs you. She deserves better. Talk to her.
I really don't think this can be blamed on depression. I have had experience with depression, with a close friend in the past. This is nothing like that. I don't know where you got the idea that she's "severely depressed" but that's definitely not the case. Our communication is very good.
You should break up with her, she doesn't deserve to be treated like that by you. Giving her an ultimatum because she's severely depressed and you cant take the time to notice she needs you. She deserves better. Talk to her.