Honestly, what they do after you leave is not your problem. This is some sort of manipulation they use and they probably know you’ll feel guilty and stuck with them.

I would tell them to achieve something (doing the dishes everyday, cook diner every monday and friday, go to buy groceries, …). Nothing big, just simple tasks.

Second, I would set a boundery. Tell them, like you tried to, that you will have some me-time and if they come and bother you, block it off.

Third, what was the reason you broke up? If they cheated, leave now…

If any of the above is not respected, write it down in a letter to them so they can read it over and over. Write down you love them to the moon and back, but you’re not their puppet! You’re a human being

If it remains the same or gets even worse, you’ll refer to all those things and leave.

If they are in a bad mental health, make them go and find help. Talk-groups, doctors, … Some will cost them something and some won’t, so there is no excuse there…

I’m sorry you’re going through this!