Catio groundcover suggestions?

I have a 3x5’ area in my catio that I’d like to fill with natives. Zone 10b, clay, part sun but on the shadier side. Would love something soft the cats will enjoy laying on or bring entertainment for them, and has to be non toxic (no poppies or yarrow). I already have a rodent problem so not a fan of woodland strawberry. I like the idea of Lippia but not sure if its soft enough, or sunny enough. Appreciate any suggestions!