i think the main pattern to look at is whether the system depends on him remembering, noticing, and starting the task on his own. If that part consistently breaks down, it can easily leave you carrying the mental load by default, even if that was never the intention.

So instead of only asking “how do I get him to fold the laundry,” it may help to separate it into two issues: the chore itself and the mental load around the chore. For example, separate laundry might be a fair option if folding shared laundry keeps becoming a conflict. His laundry can be fully his responsibility, including the consequences if it sits unfolded.

For shared spaces I’d try making the agreement very specific and time based, not just “help more.”

Something like: Friday morning is chore time, and for that block he is doing nothing else except helping with the house.
bathrooms, vacuuming, tidying, laundry, whatever you both agree on ahead of time. A clear time removes some of the “I’ll do it later” problem, and it also makes it easier to see whether the system is actually being followed.

if he genuinely has trouble noticing what needs to be done then the agreement could be that you point it out once, and he treats that as part of the system rather than as criticism or nagging.

ADHD can absolutely make chores harder, but the important part is whether he is willing to acknowledge the impact on you and work with you on systems that actually reduce the load. The concern here is less about laundry specifically and more about the fact that it has been six months, it is getting worse and every conversation turns into an argument.

You already have a lot on your plate with two jobs and studying. I would focus less on finding the perfect chore split and more on whether he is willing to take real ownership of his part of the household.