OP I could have written this...I have no diagnosis...but all my kids have asd, adhd and one has lovely combination of both one also has Pda... So I have a lot to deal with there and they're not really capable of helping me, even in there own spaces!
I definatley identify with the dishes while cooking scenario...nothing I do changes anything and I can fit a dishwasher in my poxy kitchen...have u room for one?
Although the next thing would be to keep on top of maintaining filling and emptying it...I could never.
Have you considered you might also be suffering depression..especially given the living circumstances...maybe look into that, because I have been at that level and accepting, it allowed me to not be so hard on myself.
It took me about 10 years to get some small strategies in place, not saying I stick to them but I do know they are important things and I try not to let them build to a point of being mega out of control.
My middle child (pda) is similar with regard to dirty cups and laundry the more mess the more they are unable to deal with it...cant even get in the room to do it myself as they become aggressive however I do set very small manageable targets. I ask for two or three "5 minute tidies" I only ask once a week because anything else will overwhelm them.
I also apply a similar challenge to myself. I've tried apps and reminders and notes and they do not work. If I plan to do something ill spend time thinking about it and actively ignoring it, however I'll try to put my procrastination to good use..If I need to clean the bathroom but don't want to then I'll just mop the kitchen floor etc...I have to physically tell myself right do one thing for 5-10 mins and see where it goes e.g cleaning the bathroom...sometimes I find once I get started I hyperfocus on it and tend to move to another room and continue cleaning..completely ignoring other important tasks I have that day 😅
I also have quite a messy front room but I am sure to try and give it a bit of a sweep whenever I pass through...sounds disgusting but I'll leave a broom in there, sweep most things into one corner. The small bits end up under the unit and either dustpan and brush then and there or in the next 2 days...later in the week I'll revisit under that unit with the hoover!
But I hate the faff of a hoover, emptying it cleaning filter etc I tend to leave that till very last minute!
The downstairs rooms (bar kitchen) will have a deep clean once a month because I actually feel super uncomfortable around the dirt (ironically)
(well from the floor up to mid level...r.i.p anything on a shelf)
I will wipe kitchen sides down before and after I cook because I'm in there anyway. Cupboards are a joke...very unorganised and fridge is pretty much the same..my partner will deal with those on his day off. He also has adhd though so isn't much help anywhere else that's not on interest to him because he just doesn't "see" it.
With regard to other mess I leave empty baskets in the front room for clean laundry or it would sit on my couch for a month. It's easier to find the motivation to carry a basket into another room or kick it under table than it is to look at at sitting on couch or dining table.
A second hand trofast unit was a literal life saver for toys and youngests items...I have also stopped buying and request no one else buys my kids small items..save any gifts for birthdays Xmas etc because that is not what I wanna be picking up multiple times a day and will often get swept under the couch for another day! I made a point of putting each type of thing in one drawer/box (cars, crafts and paper, large building blocks- screw lego) then shoving the couch up against it so it can't all be tipped out and overwhelm us all!
The child has to request one or two boxes at a time and I will get it out and block the area again.
The youngest (the one who make the most vile messes with food smearing etc)..actually really enjoys packing the boxes up again.
So thats a bonus (he is autistic non verbal so could not actually ask him for help but it's handy that he likes to put the box back exactly how he found them)
I do tend to have the worst of it in my room because that's where I dump everything to try and deal with it (2 months) later.
I also have to tell the children to approach me for bed changes and help with hoovering rooms and not let me say "ill do it later" it has to be done as soon as they request or I'll get distracted elsewhere.
Two share a room so i know that's 2x beds at once...the p.d.a one is more difficult so I'll have a spare quilt and pillows with cases in cupboard ready to just hand over and drag the putrid ones away from them...we've given up on fitted sheets for that child so they have thick blankets to cover mattress which they like to lay out themselves...that child is another story...
The kids also have to physically hand me uniform after school as I must wash it that minute or my brain skims over it and they will forget too.
I prioritise trying to keep them clean and tidy and fed.
I would try to give yourself a few mins to clear things...even if you start slow at one or two things in the week...for example on Tues tackle the cups/throw them out if you must and bingo that's one job done...then set a rule no cups out of kitchen.
Then say Friday you might feel able to sort throught that washing pile, check what is in there that you need to prioritise e.g maybe as its been there a while I would deal with wet things asap.
Have a think.. do u need to keep it all..if not its a good time to chuck it.
And in future grab a couple baskets and label them "priority" such as uniforms, coats etc.
One for "wet and dirty" because you'll know that needs sorting quick to avoid going manky.
And another basket for meh items that can happily wait.
The point of my waffling is basically me trying to say it is probably in your best interest to start very small and find what works for you and hopefully build on that. If it means chucking loads away then starting again so be it.
You are not alone and the fact that you want to do better is a sign of hope...hoping one day you find the strength to tackle even the smallest of jobs xx
I'll be following this thread to get some ideas myself.