Once we adopted a puppy from a high kill shelter in the midwest, who came un-spayed, with fleas, and giardia. We picked up her stool/diarrhea immediately, and none of our other dogs got it. I believe the vet put her on antibiotics.

Our other dogs did not get giardia. And neither did we.

Giardia is the main reason for water treatment before sending to homes in communities. The parasite lives in pools of water, lakes, and rivers. Healthy adult dogs can get giardia and never show any signs of having it; however, puppies do not have the immune system development. You are doing the right thing keeping your dogs away from the droppings. I suspect your puppy will recover from the antibiotics and develop normally with no more issues. If you wanted to treat your yard with something, I would use organic fertilizer. That may seem weird, but organic fertilizer feeds the beneficial soil microbes so they can fight off pathogenic microbes like giardia. Plus, giardia needs lots of water to survive and a normal yard does not have that.