Should i fix my own apartment damages?

Ok so my lease is expiring soon and, in December, management had a walkthrough of all apartments for a maintenance inspection. They sent out a memo beforehand stating to make sure all "damages are corrected" as a heads up.

I have some minor spots like where the bathroom door's first layer of paint is peeling (about one foot in length), but there is still another layer of paint underneath so it doesn't really look bad. Looks like if you popped a blister and the skin beneath it healed. So I had always thought that I'll just let maintenance paint over it when I move out as only they know the correct color or preferred paint and probably have it on hand already and it will be deducted from my deposit.

I also have a spot in my laundry room where I accidentally I guess put my Swiffer nitty gritty foam mop back without it being totally dry and as it leaned up against the wall, it kind of stuck to it and peeled up a few inches of paint the next time I grabbed it. Again, I figured this would be another pretty easy fix by maintenance upon moving out.

Both coats are white. Am I wrong in thinking that it's just better to leave it up to them or should I actually go out and buy paint and do it myself? I don't think they're out to get me, but I am uncertain of what the common expectation is especially based on their memo they sent in December. Rent here is in the $800-1000 range and my previous apartment was only 450 when I left a few years ago so the quality and expectations may be different.

Please give me some advice.