Sorry, if it isn't a carnivore or something someone or animals can eat, its a weed :) Especially if you can walk on it without harm!
I removed half my lawn and replaced it with blueberries, daylilies, haskaps, more daylilies, azaleas/rhododendrons, lilies, lilacs, raspberry/blackberry hybrids, a couple more daylilies and some Heuchera. Had too much lawn and mowing took forever! Now, I don't feel like I'm wasting time on weeds ;)
Your esseriana are gorgeous! I wish mine were so happy.