I have bipolar 2 and clinical depression. I usually have about three weeks of depression a month - some months are worse than others and I don't get any 'ups' at all, sometimes for several months at a time. Those are the worst.
I completely understand what your going through. Finding ANY motivation, even just enough to clean your teeth, is just SO hard! I have times where I go several days without showering, basically until I just can't stand the way I feel enough to have one. Or, if I have to go somewhere that I can't get out of.
Sometimes, I can't concentrate enough to read. Or even watch television. I sometimes sit in the same spot for hours, just staring into space - that's when I know I need to take additional medication.
I have several pets, so I do have to get it together enough each day to feed and water them, make sure I have enough supplies of what they need etc. They keep me going and I'd be in big trouble without them.
I don't really force myself to do anything I don't absolutely have to do. I wait until motivation strikes again (and it always does, even if fleeting) to do anything non-critical. I often feel embarrassed and ashamed by the state I let myself and my home get into - sounds weird, but I'm actually incredibly fanatical about my house and my own personal grooming. But only when it comes to others seeing me or the house. My home is clean and hygienic because I have a cleaner (I have to, my mental health would be even poorer without it), but when I'm in a slump I tend to let things get untidy. Take things out and don't put them away, leave stuff lying around, don't pick up the animals' toys, don't make the bed, etc. I usually spend 20 mins tidying before the cleaner comes instead.
Absolutely nobody knows how I live. They'd be horrified if they did! My family especially. However, they know not to visit without asking first and they also know that I sometimes need to switch my phone to voicemail because I can't handle talking to anyone. They know they can check on me via text message and I will always answer. Same if there's a family emergency.
I also try to spend a lot of time in nature, even if it's just sitting in the garden. I live in the country, so I sometimes jump in the car and drive somewhere quiet and beautiful. I find nature comforts me more than just about anything else.
My point is that you need to be kind to yourself. It's SO important. Take the pressure of yourself by not constantly picking on yourself for not doing non-critical things. So what if you don't have a shower for a few days, if you're the only one who has to smell yourself? You won't die! So what if you can't do the vacuuming? I sometimes have cat hair tumbleweeds in my house!
Nurture yourself, be gentle with yourself. If you don't put pressure on yourself, you'll find that your motivation for life comes back quicker. Nobody ever died from not hoovering for a couple of weeks.
Blessings to you - go gently.