Thats why you need to protect the wood from the wet soil. Or use special wood thats fit for wet circumstances.
You also need a good overhang against the rain.
To keep the inside dry you need to make lots of ventilation.
There really is no need to use high solid paint. My cheap prefab coop has a fungi paint with linseed oil on the outside and DE on the inside. It needed a new and larger roof, and a new lid on the nestbox, but otherwise this coop exists 12 years now.
You may have missed that my coop is "at grade". It's a 10 by 10 "kit" shed sitting on the ground that I bought from a "big box" store close to 30 years ago. It was rebuilt and re-skinned (and re-floored) about 5 years ago.
The "floor" (now) is several pieces of 4x8 heavy thick white plastic that is intended to be used as a vapor barrier for basement walls... held together with Liquid Nails adhesive.
The coop is also very well ventilated with automatic crawl space vents on each side (at the top)... and a solar powered roof vent on the roof peak.
There is also a window on each side for "pass through" ventilation.
If the coop gets too hot there is also a 10x10 coop extension off the East side, opposite the sun and outdoor run. It was a dog kennel I found on Craigslist.
Believe it or not... all my birds got along. However the Guinea Fowl had to go. (They got on mine and my neighbor's nerves, and my neighbor worked night shift.