Root rot. That spot might be low and holding moisture longer than the surrounding area. My go-to product for St Aug fungus is ordinary corn meal. Corn attracts another fungus that consumes the disease fungus. The application rate is 20 pounds per 1,000 square feet. You can get corn meal or cracked corn at feed stores. You can get corn flour at grocery stores that cater to the Hispanic community. Price is high this year. It might be higher than $10 at either place. I've seen corn selling for $3 per bag, so it's definitely a commodity with worldwide demand. If you want to use a chemical fungicide I can't help you pick one that works. There are others here with fungicide experience who can help you.

This needs to be fixed asap. You have some bermuda in one of the pictures. The bermuda will take advantage of this and move in. Once the St Aug is healthy again, it will overtake the bermuda. Keep the grass mowed at the mower's highest setting and don't water more often than once a week in the summer.