How do I get items after they fall into the water?

Find something large and metallic, like a metal box or chest, and use that to push the thing you lost to the shore.

Cryonis will only create ice pillars starting just below the surface of the water, so it won't "push up" anything that sank.

You currently can't dive in Zelda. So if something falls into the water and you can't pick it up while swimming over it you are out of luck.

The only solution how you interact with items below the water surface is the magnesis tool. So you can try to drop a magnetic weapon (or search for something magnetic) and try to "fish" with it, to push it to the beach and pick it up from there.

I created a cryonis slab near the underwater gems (but not TOO close or you can't see them or hit them), then used stasis on them one at a time and hit them with arrows to project them into shallower water so I could pick them up. A Lynel bow or Duplex bow works great because you get more hits with less arrows. Also you can pick up your arrows when you're done, as they float to the surface! Hope this helps!