I too think you are doing a great job, I think you have to pick your battles to some extent, but I agree, I just couldn’t bear the mess, It would really drive me nuts!
Could you bear to let him do whatever he wants in his own room, wash your hands of it, but absolutely insist that common space is tidy, eventually, he might even decide to clean up.
Washing is trickier, he obviously has to go to school clean and tidy, so it’s got to be put in the washing machine by somebody!
Honestly though, he’s still only a little boy, whose had a very difficult time, and so have you I’d imagine, be nice to each other.