There is nothing wrong with using play sand. It is extremely fine and smooth so it is not much good for grit. They will still eat it and try to use it as grit but it will pretty much go straight through their system. I find that play sand, since it is so fine, sticks to my shoes more than coarser sand and can be tracked around, especially if my shoes are a bit wet. Probably not a big deal for most of us. It still drains very well and will work in a coop or run. Since it is so smooth, it will not hurt their feet.
To me, the river sand sounds like a good option. It has larger grain size so it will not track as easily and will not pack as tightly. It does have the pebbles which they can use as grit and it is rounded, so they get a smooth footing. Construction sand would work, but since the grains are sharper than river sand, there is always a chance they could get bumblefoot from it. I built my run to include an area where I had a small pile of construction sand and mine have never gotten bumblefoot, but I was concerned about it for a while. Maybe me being overcautious or overthinking it. Construction sand does make great grit for baby chicks.