Is this something that a landlord should take care of if asked?

I have no knowledge about the responsibilities of a landlord so I’m coming for you ladies for help!

This is our to-be nursery’s bathroom ceiling. There’s a shower that my husband uses and no windows or air circulation (the thing on top should circulate the air but it doesn’t and never has).

My worry is that the ceiling is getting moldy or something and I don’t wanna use this bathroom for my baby if it’s a health hazard of any level. It seems like the moisture has messed up the ceiling a bit and there’s def a circulation problem.

So my QUESTION: Should my landlord be responsible for painting the ceiling/renovating the bathroom? I’m not saying give us new appliances and brand new shower, but a renovation or upgrade of any level.

Thank you!!