Most of the time, when I create rectangles, the vertex editor icons in the left column remain grayed out. I can't use them. Once, they showed up and I used them. I've looked through the forums and checked all my settings. I can't figure out why they won't show up so I can round a rectangle's corners.

I just found the answer, I think. If I use dual layout (mobile and desktop), the vertex editor isn't available.

In dual layout, it is available only from the Objects tab. There the edits will change both desktop and mobile layouts together.