Well, I think that cleaning is a skill set like any other job. And like any job it requires executive functioning skills to carry out. Add to that many people aren’t taught how to keep their living space clean or why it’s important to do it. It sounds like your partner cares about you. I can’t remember if you mentioned in your post if you’ve talked to them about how this is effecting you?

That’s your first step. You should gauge their willingness to learn. Second there’s tons of apps and you tube videos that teach on the subject and apps with checklists to complete and reminders can be entered. Basically free resources that can help him get into the swing of things.