Q.St. Augustine grass runners
I have purchased a new (old) home with predominantly St. Augustine grass. Many of the runners are growing over the top of the surrounding grass and not in the soil. I don’t want to cut them off when mowing and would like them to grow in the soil. Any suggestions as to what is causing this and what can be done to correct it?

The runners are supposed to be there in St Augustine. They’re called stolens and that is how St Augustine spreads.
This article will help review the care of your lawn.
https://www.gardeningknowhow.com/lawn-care/specific/st-augustine-grass/st-augustine-grass.htm