yes, Sherwin Williams makes paint for bathroom use.

So does Benjamin Moore and other manufacturers. You probably want an eggshell, not a flat wall paint for a bathroom. Also look for/ask for a paint with mildew prevention additives.

Do you have and run your bathroom fans for a minimum of 30 minutes after every bath and shower??

We do. Sadly it’s not enough for o prevent the water mark streaks. Sigh

I would use at least satin finish in that bathroom. Maybe see if that fan vent is also vented out through the roof and just not putting all that humidity into your attic. If it is vented to the outside, then, maybe you need to invest in a more powerful vent. That much humidity after a shower, and a fan running, is just way too much. Also, after the shower when you leave the bathroom, do you leave the fan running and the door open? If not, you should.

We do. The wall I took a photo of is a good 8 feet from the shower. It’s the same thing in every bathroom including the laundry room.

Have you been in the attic and checked to make sure those vents are vented out through the roof? If they are, and you run them often, then, you most likely need new more powerful vents.