Difficulty in returning a property to landlord

I have lived at an apartment for 5 years and a half. Recently, I bought another apartment and moved out. Specifically, I told the landlord in Feb 2022 and moved out in June 2022. I've always paid on time.
Now one week ago, the landlord had a contractor to come to the apartment and estimated the repair cost. Then he sent me an estimate with a lot of money (four months the monthly rent). He told me that I had repainted the apartment, the bathroom door is not functioning anymore, and there are dirty stuff (walls, floors, bathroom).
In fact, I did not repaint the apartment, I told him so and asked him to check again. Then he now mainly focused on the stains on the wall. In deed, there are several stains, and after more than 5 years, the walls are not the same as the beginning. But I think asking me to repaint the entire apartment is not reasonable. Second, the bathroom door is functioning (not broken), but of course it becomes old because of time and normal use. Basically, we have a disagreement regarding the repair of the apartment.
I have paid the rent for June, and already moved out. But the landlord said he cannot accept the handling of the apartment (remaining keys, because has already took back a key). He also doesn't sign the 'etat de lieux'. He told me it has to be done later (maybe end of July or even August).
I have the following questions:
- What can I do? I still have the keys to the apartment. How to return the apartment in this case?
- For July (and maybe other months if the problem is not solved), can he charge me any rent? To me it seems unreasonable because I'm not using the apartment anymore, and gave him the notice 4 months in advance.
- For the cleaning of the apartment: I tried my best to clean, but couldn't satisfy him. But as far as I understand, he cannot ask me to pay for repainting the entire apartment. Is that correct?
Many thanks.