Check out the following plants: Purple queen, oyster plant, bromeliads, baby sunrose.

It might be hard to grow much under there. Usually the ground cover I see here under evergreen oaks is a good thickness of their own dead leaves. Even weeds find it tough in dry shade.

Mondo grass, liriope, Kimberly queen fern, foxtail fern, asiatic jasmine

Our neighbors in Florida use Asiatic jasmine.

Bromeliads made a nice groundcover under my live oak. They looked a lot like these and filled in densely over time:

Purple queen.

Asiatic jasmine

Asian Jasmine shady gardens · More Info

Tradescantia

I had royal ferns which are large and attractive, but they spread much too easily, even tho they're not hard to pull out, I couldn't keep up with them and they gradually took over too much space.

They all got killed by the saltwater storm surge of hurricane Helene last fall, which was kind of a relief.

Oyster plant

Here are bromeliads and a hanging orchid under one of my oaks.

Here is the back side.

Ferns love it.

FWIW, oyster plant can be problematic, if you don't like keeping up with lots of volunteers. Their seeds seem to be invisible, but easily spread far and wide. In fact, that's how I obtained mine in the first place 😏

In south Louisiana, Asiatic jasmine is often under massive live oaks, as mentioned above. I’m not a fan of how aggressive it can be, but if you don’t have adjacent flower beds, but more bare zones, and you weed-whack it every year or so, it could work. You could also nestle large pots of ( something appropriate) in there, though the jasmine could invade them.
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Asiatic jasmine is the classic solution under live oaks. You need to plant it in small plugs, mulch thoroughly, and water consistently after the first year or so you never need to tend to it again.