Do have an exhaust fan in the bathroom? If you do, use it. It Looks like they used flat paint. I would repaint with at least eggshell, but preferably something with more gloss. The problem with glossy paint is it shows more defects in the tape and mudding. That’s one reason why builders use flat, the other is it’s cheaper and easier to paint.
Let me see where your window is leaking. We had windows leaking for years. When I repaired them after repairing tornado damage, I found the windows on the second floor were not flashed correctly and the builder didn’t tape and wrap with house wrap. If the builder doesn’t flash, tape and seal the windows with wrap, you will continually have leaks. The tape and flashing keeps the water on the outside of the house, and not the inside.
This is how you correctly flash a window and how i did mine.
I will take a picture of the window tomorrow. The first time it leaked it was like a water faucet was on. After the initial fix, it turned into just dry wall stains under the window after heavy rains. The last guy who came out couldn't even get the window sill off due to all the caulking. I'm not handy at all, but it blows my mind that its leaking after all the stuff they have tried. They are gonna water test this time (after I have suggested that the first 5-6 times) and hopefully find it.