I think there are (at least) 3 different things going on for you.
Firstly when dp's kids are there the mess and choas drives you to distraction, you feel overwhelmed and exhausted. Although dp parents them, his approach is more relaxed that yours (for whatever reason) and he doesn't enforce boundaries that he knows are important to you. Are there things that he / you both can do to change this? my neurodiverse dgc have detailed lists to follow. Not just 'get ready for bed', but take your clothes off; put your worn clothes in the laundry bin etc. Not just 'clean your teeth' but put toothpaste on your brush, (and finishing with) wipe the sink to clean up toothpaste spit. His dc may require different things but is there an approach you can agree on to minimise the chaos? There is also a high energy 15 minutes of frantic tidying - with a timer - whenever things start to get a big messy, one chiild puts the lego away, another helps with laundry etc. Bottom line here is can you and dp work together with his dc and yours to find strategies that work, and which alleviate some of your stress and distress?
Secondly, the actual relationship between you and your dp. You say you love him, but your posts read as though you are quite disconnected. He's gaming, you're in bed, you find it hard to persuade him to do things together with you. It feels quite depressing. What can you both do to continue building a positive relationship that serves you both? Life with 4 children is going to be challenging for any family - blended or not - but you get through it best when you have a solid and thriving relationship between the adults. Do you have that? If this is your life now, how will it change in say 10 years time, when perhaps all children have left home? Will you be embarking on adventures, laughing at ridiculous things, or will you be in companionable but lonely silence? Will dp's messiness make you wonder whether you'd have an easier life on your own? Bottom line here is do you and dp really have a realtionship that is worth fighting for, worth dealing with the challenge of 4 kids in the meantime? Can you work together to make that happen, or after 5 years have you both lost interest a bit?
Thirdly, your own ds seems to enjoy being part of a bigger family. I wonder whether you feel some guilt that he is an only child, and that the ready made step-siblings seemed like an excellent part-time solution. Few sibling situations are perfect - competition, bickering, different neurodiverse issues... but I wonder whether you / your ds are tolerating a level of disruption or low-level unkindness? If you were not with your dp, how would you bridge the sibling space? Would you have more friends to stay over with your ds (after all you'd have the room for them)? Would you find groups and clubs for him to join (you'd have the time to take him).
It feels like all 3 of these issues are conflated. Maybe if you consider them all independently you will have a clearer idea of what you should do...
I've not included the financial situation in all of this. It sounds like a complex overlay. It reads like you could manage OK if it were just you and your ds, but your dp is quite dependant on the status quo in order to afford living 50/50 with his dc (each in their own room), and to assuage his guilt and pay his ex. If that's the case, he is going to be pretty resistant to many of the changes that people have suggested. Be prepared for that.