I struggle too when I am having a bad depressive episode.

The Timer is a really good idea. I do the 20/10 method when I have a lot to clean up, so 20 mins cleaning 10 mins rest (repeat as many times as I can manage). Also I found the habit of making my bed every morning and doing the dishes before bed every night beneficial, doing just those two task even if I don't or can't do anything else in the day makes me feel like I accomplished something and thats a pretty good feeling on the rougher days.

Good luck, I hope things get easier for you soon