There are a lot of different sized runs built in a lot of different conditions in different climates. And we manage them a lot differently. It’s not so much that there is one right answer for everyone and everything else is wrong. It’s more of what works for you in your unique situation. One consideration is how wet your climate is and if water drains to or from your run.
Some people, especially with small runs in suburbia use mulch-like stuff like shavings or straw and just change it out a lot if they have wet weather. I don’t do that but it works for them.
Sand is a great material for the run. It drains really well as long as the water has a place to drain to. If you are in a low spot, nothing may work well. Sand has some potential problems though. It can work its way down into the mud over time. You may need to occasionally replace it.
If it is built up and not contained, a good rainstorm may wash it away. Also your chickens will love scratching in it. They can scratch it out of the run. To solve both these potential problems you might want to put some type of border or containment around the inside bottom of your run.
My run is just dirt, but it is on a small rise so it drains pretty well and I put a swale on the uphill side to divert rainwater away from it. When it sets in wet for a while it does get pretty muddy but it’s hard to keep a big run dry in wet weather.
Good luck!