What groundcovers could I plant around the bases of fruit trees? It should be something I can step on as I harvest fruit, and something that won't harm the tree or be harmed by the shade.

I have Geranium maculatum planted under a giant apple tree in my back yard. It does well in shade, blooms for
several weeks in late Spring, will stay green until frost if the ground is kept reasonably moist or will die back
to the rhizomes (which spread slowly) if allowed to dry out, ready to arise again next year. It is altogether
charming. I don't know how it would fare in Austin.

You really dont want ground cover around fruit trees. they are so sensitive to fungi and bacteria.. I hate the words "clear cut" but fruiting trees should have a clear cut the same diameter as their crown.

Fruit trees are better left without anything around their trunks since they don't like the competition: grass is fine, but that's about it.