I've been completely overwhelmed by my place and have turned things around. I was no where near as stretched as you are OP, but here are my thoughts on this.
You have high expectations of yourself but little time to do anything. So all the undone chores become sticks to beat yourself with. This adds to your burden.
You are exhausted and tired which is not surprising.
You have way too much stuff - this is evidenced by the piles of stuff on top of each other. You will no doubt have doubles/triples of things as you buy again when you can't find what you want/need. I think accepting you have way too much stuff is the key here.
What are all these papers you need to file? Switch all your bills to online/paperless. Bank statements too. The as post comes in, read it and put it in the recycling (I take the address details off to shred). File only the very essential and if you insist on keeping copies of bills, keep only a years worth max.
Your teens need to contribute A LOT more - with what they can cope with, but you do need to push them. It will be easier for them to engage once the place is sorted out.
You need help or time = preferably both. It will be hard and lots of work but I promise you your energy will soar after doing this. I think you need a week off work to give this a big push.
Start with the kitchen = it is the energy center of the home & getting it sorted will have a knock on effect. If you accept you have too much stuff, so much will be thown away it won;t be a 5 day job. It would be if you keep everything, but this isn;t the answer to your problem. What you decide to keep will be comparatively easy to keep clean and tidy.
Decide what you need to KEEP - because you LOVE IT (truly), NEED IT (as in really really need it and nothing else can do the job) or USE IT. Keep essential kit only. Throw out everything that is past it's use by or best before. Be ruthless, really really really ruthless. remember your objective isn;t to keep every spice known to man (threw out 3 supermarket bags of spices - found it really hard, but it hasn't actually affected me at all, cause as I couldnt locate spices when I wanted to use them I usually just brought more anyway), but to restore your kitchen to being a workable, functioning pleasant place. This will not be possible if you think you have to keep everything. Also throwing stuff out is actually quite easy and once you get going it's fast.
Re crockery etc, think minimally. Keep what you Need, Use, Love but only that. You only need one garlic crusher, grater, lemon squeezer etc. Stick to the basics - if you've brought novelty things over the years you don't use, get rid. You cupboards will feel empty - but this is good. You will be able to see all your stuff, and you will use them more. Because you will be able to see them, find them.
Remember all the while that what you value about everything is space - clear space. You really won't miss anything you have discarded or donated. I promise.
Be ruthless. Be fierce. Think of clean clear spaces.
Have a space for everything - why cleaning products everywhere. keep minimal stuff - surface cleaner, bleach, etc and keep under the sink. You don't meed a million cleaners, you need a couple of all purpose products that work well and some gloves and microfiber cloths.
If you are buying food you can't put away do you need it? Are you buying too much there too?
Once you have kitchen sorted, and cleaned, keep surfaces clear. Only absolute necessities on the counter. Your goal each day is to get back to this "ground zero".
Keep things in their place - if you mend socks in the car why are they in the kitchen? Keep them in a bag in the car.
Getting your kitchen down will energise you. Then you will start to look at other places with a fierce and energised eye.
It does sound as if you have too much overall. It is all too easy and a common situation to be in. You need to minimise everything - get down to the bare basics. The less there is in the house, the less there is to use, to clean to store and to make a mess with.
It is really easy to be attached or overly connected with this mess/stuff. But I promise you once you find a way to break through, then you will find a way to
do this. It will be hard but it can be done. And you will feel better afterwards.
Only you can take the time off to do this.
If you can't then I would suggest taking those small moments and using them to fill bags for rubbish/recycling/charity. Leave the cleaning for down - do that once you've got rind of all the life clutter.
If you get slowed down by thoughts of It's a waste/I should ebay or car boot these items/I will give these to XYZ, then you are losing sight of your goal which is to GET STUFF OUT AND FAST and CLEAR SPACE. It's an emergency situation - stay focused and you will make progress.
Hugs and hope you are feeling better soon.