That's kind of the way chickens and other livestock have been kept for thousands of years. You don't want the poop to build up because that can stink and poop build-up can lead to diseases, so there are limits. It's been more recent where chickens are now considered pets and people that never grew up with chickens, horses, cows, or other livestock and keep pets like dogs in the house that people have become obsessed with cleanliness. To me that level of cleanliness is not natural but there are many people where a high degree of cleanliness is desired. Obviously the previous owners did not share that. Even if you consider them livestock there are limits. I don't know how bad what you have really is. I suspect I've seen worse growing up in a small farm area all those decades ago.
If it were me I'd check for mites and lice, maybe get a vet to check a fecal sample for worms. Check to see if you do have a problem. If you do, deal with it. As for cleaning I'd scrape the dried poop off, either a scraper or a wire brush. Wear a face mask, that dust is not good for you to breathe. You may want goggles. Take a bath afterwards. I don't know how conducive that area is to actually washing with soap and water. To me that would be unnecessary and may not be practical anyway. That may be a pretty large area.
I personally would not try to disinfect unless I was specifically treating something. As mentioned, they have already been exposed to anything present and, if they are healthy, their immune systems are strong enough to handle it. If you do use anything to disinfect it, air it out well before you allow the chickens or ducks back in. Maybe even set up a fan to clear it out. Poultry have sensitive breathing systems and can be affected at fairly low concentrations. You don't want to harm them by truing to help them, especially when they don't really need the help.