All true statements above. Fix the issue or move the coop.
We also had drainage issues-I live in a fairly flat area of Ohio. Water wasn’t draining very well, and the whole back area was a squishy mess with rain, and some areas had standing water. The area the coop was in would mildly flood. So, we built an elevated walk-in coop so it wasn’t directly on the ground. Then we added flexible drain pipes to the gutter downspouts to direct water flow where we wanted. Then we had 102 tons of dirt (4truck loads) brought in to spread out and make the back area flat (actually not the coop and run area, but area around it where our raised bed garden was going to go). In the run area we put approx 20 yards of chunky chipped wood and we lined the run fence with 2x4s one level high. These kept the chipped wood in the run. The run is 500sq ft and is bordered on one side by our barn. Now (a few years later) we finally got the whole run roofed. Rain still blows in, and we don’t have gutters on the roof over the run, but the run no longer is a wet mess.
My neighbor had a similar problem. His solution was different. He dumped a lot of gravel into the run and spread it out. He topped this with straw snd chipped wood and more straw. His chickens stayed dry after that. He had NO roof over the run, just a couple old sheets of plywood here and there, so his run wasn’t very protected from the rain.