Have a frank and honest conversation. Clearly the current system isn’t working so each person needs to wash what they use and the new arrangement needs to be no dirty dishes left overnight. If you have a dishwasher then run it every night if y’all have to, it will actually save money to do so compared to hand washing. And don’t fall for “I’m letting it soak overnight” as no dirty dish ever actually needs to soak that long.

In the same conversation, make it known that this is a deal breaker when it comes to renewing the lease. No change in their behavior means either they will be looking for a new home when the lease it up or you both will. Sometimes the only way to deal with a bad roommate is to no longer be roommates.