That appears to be straw and not hay. Straw is best suited for areas that stay dry which appears to be the case with your run since it has a roof. Straw is less likely to mat and mold than hay so it should be okay, but keep an eye on it and remove wet, moldy areas.
However, I had one run that i felt large enough to put out molded hay & straw. The chickens then spread it out, breaking it down & then it composted nicely.
Did not appear to cause any issues.

Already spreading it about...


I have done this many times since but no pics...