God there are some unhelpful responses here from people who have obviously not been in this situation. OP, I've been there.
There is good reason that the advice about toxic people is to go no contact, just cut them out of your life, or go as low contact as possible. The more contact you have with them, the more opportunities to feel irritated by them, bicker, be abused, all of which creates stress for you. There is little chance for productive engagement with these people, interactions will almost never go as you hope. So just reduce the interactions.
@Garlicnaan is right, the biggest shift you need to make is to decide you're not going to allow him to affect your mental state.
You have to accept that he is who he is, he's going to be a dick about lots of things, and there is absolutely zero value for you in engaging in conflict with him or trying to change who he is. Your one and only goal is to protect your own peace of mind while you're stuck in a house with him, so you are going to want to do whatever it takes to avoid conflict, which will only cause you stress.
You have to let go of ideas of fairness or being right, and take the high road/ a more practical approach. In a year's time, you'll be a single mum and doing everything by yourself. So start doing everything now and stop complaining about it. Yes, it's extra work for you but it's good training for the future.
If a messy house fucks with your peace of mind, pick up his stuff and put it in a pile in his room rather than starting a fight trying to get him to pick up. It's easier to do it yourself than fight over it, honestly. If he's never pulled his weight, stop expecting him to or trying to get him to. Just do it yourself, and work on making your systems more efficient so you can get everything done by yourself. Yes, I know it's unfair and it feels like pandering to him, but it's picking the better of two bad options.
Every time I did something that was really his job, I told myself that I was becoming more capable and independent and he was becoming weaker and more reliant, and it was going to come back to haunt him. Now I smile every time I remember my ex moaning to me that it took all weekend to clean the huge new house he rented after we split and that "it seemed to be an unusually dusty and dirty house". No, dude, that's what all houses get like when you can't be bothered to clean them regularly.
Never show up to a fight he invites you to. I always think of that meme with Tom Hardy as Mad Max where he shakes his head and says, "That's bait". Learn to recognise bait and don't take it. When he provokes you, say "Oh, okay" or "That's interesting" or "I'm sorry you feel that way" or "You may be right" or whatever mild, non-committal response makes it difficult for him to argue with you. You don't have to mean what you say, you just have to say it. In your head you'll be thinking, "Christ, you're a moron and I'm not going to dirty myself rolling around in the mud with you."
I shifted my sleep hours so they were right out of sync with his. Started waking up very early so I had time for myself in the mornings before work and then going to bed basically as soon as the kids were in bed. This minimised direct contact.
I focused on doing things with the kids that they and I enjoyed and he didn't. Planned more outings, even trips away to places he wouldn't want to go. Lots of visits to my parents house while making it clear that if he had "other things to do" it was fine if he didn't come. Spent lots of time making plans and spreadsheets and counting savings as I worked towards my exit point.
It's all worth it. In two years you'll look back and be amazed at how your life has changed.