I mowed the grass a bit short and when I did this was what I got. The neighbor's grass is same. Brown towards bottom but top is green. Just unhealthy? Combination of St Augustine and I believe a type of Fescue.
I did not even consider that because that's the last thing I would have expected but seems you may have nailed it. The neighbor keeps their grass high and that may be the reason for it.
I know absolutely close to zero about the growing habits of your grass combination St Augustine and Fescue. If that was bermuda it could be taken down an inch with a sod cutter, sell the sod and that would be the best thing that could happen to it.