I could not zoom in on your picture but I did see leaf miner, the squiggly line in the leaf on the lower right of the shot. It causes minor damage. If you can find the larvae lump at the end of the trail squish it.
The leaves look chewed and are most likely to be slugs or snails. Look for slime trails. They will hide in a dark moist places during the day. You will most likely spot them in the early morning or at night with a flashlight. I put slug bait in a pot or can and turned on its side in a shady spot. Don't put slug bait on the plant. If you have a dog, get sluggo or worry free, they contain iron phosphate instead of metaldehyde and don't look like dog food.
The browning at the edges of the leaves look like some kind of stress. It could have been from the transplanting or water stress.
I cannot tell how deep the box is and how close the eggplant is to other plants. Eggplant can get quite large so it needs space. I keep mine in 16-20 inch pots.
You live in zone 9b so it does not freeze which is good since eggplant are very susceptible to freezes. It is unusual to start an eggplant at this time of the year. It is a sun loving plant and does better in the warm season. Hairy plants like eggplant and tomato need to be on a fungicide preventive program during the rainy season. Neem oil every week does ok as preventive but won't work as well if you have a problem. In a frost free zone eggplant can live for a few years, but I replace mine after about three years because the production declines.
Use the finger test to check if you need to water. Depending on your soil and weather, watering schedules will need to adjusted. If the top of the soil is still moist you can wait. If you poke your finger in the soil and it is still moist a couple of inches down you can still wait until the soil in the root zone is almost dry. Mulch and a lot of compost in the soil will hold on to moisture longer.