Q.Grasses That Grow In Shade Where St Augustine Won’t Grow
Grass won’t grow in bare spot

Certified GKH Gardening Expert
Getting grass to grow in shade is often a problem. Interestingly, according to the Texas Extension article below, St. Augustine is the most shade tolerant warm season grass. If it is under a tree, mulch looks good and enriches the soil. I suggest contacting the extension office for a recommendation.
Some people go with an alternative to grass: shade groundcovers.
https://www.gardeningknowhow.com/lawn-care/lawn-substitutes/lagen/lawn-alternatives-warm-areas.htm
https://www.gardeningknowhow.com/special/xeriscape/drought-tolerant-ground-covers.htm
https://www.gardeningknowhow.com/special/shade/ground-covers-for-shade.htm