This is ever so sad.
OP I’m a step parent myself and yes, the kids do drive me mad sometimes with their mess. Similarly to your partner I moved in when the children were quite young. And I did crack down on the living room and dining room in our small home being a giant toy box myself, it was completely out of control and there were more broken toys than workable where nothing was being looked after. But it was a thing where I got the kids on board to do it with me (storage solutions and what could be donated, what couldn’t be salvaged), redecorated their bedroom so that they’d actually enjoy playing in there, a new desk area downstairs for crafts so we didn’t have paint on the carpet again, not a unilateral ‘nothing comes into the common areas’. There is a way to get a less messy house and bullying isn’t the way. You can make effective change with kindness.
that being said it’s too late for your partner to change and suddenly be kind to your son, if he was going to be a decent human being he would be by now.
I don’t imagine you leaving him is an option, or you’d have done it before you had a child with him.
is there a chance your son can go to his father as the primary residence? I know this may not be what you want, and yes your son may see it as being pushed out, but for his own mental health he shouldn’t be living under the same roof as someone who’s unkind to him. It’s so damaging.
I would suggest therapy for you to try to understand why this has got so far. Are you frightened of him? Just a very passive person?
i’m nobody to judge but as a step parent, not even biological, if I ever thought they weren’t physically or mentally safe with my DH I would not hesitate to get in touch with their mum to come and get them. If I suspected their stepdad at mums house was like yours, I’d fight tooth and nail for them to be here permanently, but I know their mum would not let this happen to them. When you are responsible for children - as parent or step - it’s the adults job to make sure they grow up as least fucked up as possible. Do the right thing for your boy. If you can’t leave DP then your son needs to go where he’s emotionally safe.