That is healthy looking St Augustine. Since you are in FL I suspect you are watering the lawn wrong. I say that after reading several lawn forums for 14 years and noticing that FL and SoCal owners have the wrong idea about water needs. More on watering later. Quite often the only problem with a lawn is improper watering. When it used to look great but slowly turned bad, fix the watering.

You might also be mowing too low. St Aug should be mowed at the mower's highest setting on a weekly or fortnightly basis. It should grow just fine in sun or shade.

Some time in the fall you should rake up the oak leaves and compost them. Live oak leaves are too small and too tough to mulch with the mower at the high mower setting used for St Aug. Then you can spread the compost wherever you like. If you leave the leaves on the lawn they will cut off the free flow of air around and through the grass. St aug will get diseased in a day or two if you leave something on top of it that cuts off the air.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

Thank you!!!

To be perfectly honest we haven't watered the lawn at all. My spouse mows too low. I know it, but he is starting to see it. He scalped it when we first moved in. It's slowly recovering from that. I wasn't too worried about it recovering because we were going to replace it. The plan has changed.

Do the first pictures appear to be the same variety as the last? I only care because it might look weird to have different varieties mixed if the blades are very different. I was thinking of mixing microclover in it to help provide nitrogen.

If you are OK with microclover mixed in with SA grass, then I'd be surprised if you would mind the aesthetic quality of two different varieties of SA. No idea if you could mix clover with SA...

Are the tips really pointed in some of the grass, or are the blades just partially folded?