Wow this was eye opening for me - just as I suspect I am autistic and this was so me to a tee as a child. Also I have an autistic daughter and help support parents with children with challenges - I just hadn't realised "this" was quite so clearly me in this area.
I have a 12 year old with asd and I know the frustration when it seems they just wont. I dont at all doubt you're a dfab mum and have tried so hard. I really hope some of this can come across as different approach rather than criticism in any way.
The recent advise has been fantastic - imagine she was in a wheelchair/what would your expectations be. Read the responses geared at those wtih asd or focus on her not being able rather than unwilling.
I think too focus on the child you actually have rather than a "hypothetical what an x year old should do." You have a child who finds self care such a struggle she will get upset about it. This will be affecting her deeply.
Try to have time away from "the battle. " She will be seeing you as another source of tension - do fun stuff together or sit and watch somethinf you like etc. Make sure you remember all the lovely things you love about her. Both you and her can get so focused on the bits we cant do and it can be very depressing.
Change of perspective. Yes it is incredibly hard for you, more so than parents of nt kids will ever see, the constant striving with it all and trying to do your best etc. But if you can see at these moments that she is a child struggling just as much, and is a child who needs support - it can help diffuse a situation. I have to remind myself of this often...
Choose your batlles - you cant do this all at once. Realistically she's a teen so not long left either.
What can you support her with first? Think of it more as an investigation into why it's difficult (she may not tell you. She may not know...) and try and find ways to support.
I know a story of a child told to "tidy his room." But didn't have the executive function to do this and would end up playing etc which is all the parent saw. Not the distress. And then upset at being told off. What worked for them was photos of how the books looked neat pinned next to the bookshelf etc. This wouldn't work for others. Every person is different.
With clothes. Some find this completely overwhelming (I still do..) and my teen can not be handed a pile of clothes to "put away." If I sit with her or say "can you put these leggings away in your drawer" she can.
Breaking tasks down into small achievable steps can help - ie the leggings not the whole pile.
Having an attitude of putting things into support her rather than to criticise or nag (which as you've seen doesntwork anyway) as you go through each issue will help so so much.
It maybe each night/afterschool whenever they get changed you need to ask for the dirty clothes. Not in a judgey way but in a "ooh canyou just pass me the clothes from today. Way."
My daughter (and mysefl) get very very overwhelmed with a messy room. Yet also lack the executive function to sort it out. So will sit distresssed and then be unable to do other things.
Anything you cam put in place to make life more ordered and less stressful will help. Help night before to lay clothes out for the next day is a big one. (And not being told to do it/getting cross but positive encouragement.)
The thing mentioned above about positiviry is so so important. Nagging or threatening will just cause fear (of not being able to do it) which can trigger a further shutdown.
There isnt a one-size-fits all answer. It will be individual to each person, but these are familiar areas of struggle for autistic girls. It is so worth approaching it together as a thing to face together rather than as a nagging parent.
Also for her own self esteem if she can find out about autistic girls it might well help for so many reasons.
If you read there's a book I recommend as an easy read called "Can you see me?" Written by a young autustic girl and a writer. Her issues will be different from your daughters but it really helps to see things from their perspective. And if you can hold that on your mind when you deal with them it will help so much.