Grasses are difficult to identify and Extension Master Gardeners are not the best at knowing grasses.  So I cheated a little and used two different plant ID apps (PlantNet and Google Lens) and they both said your grass is Little Barley, Hordeum pusillum.   However, it doesn’t look quite right when I looked up that grass.  IF it is this winter annual, then the herbicide you used in summer would not be effective.  Winter annuals germinate in the fall and so a pre-emergent applied in September would be most effective.  It does look like some type of bunch grass and a broadleaf weed killer would not work.  Killing a grass in a grass lawn is hard. If you can cut off the seed heads before they ripen, then over time you will at least slow the spread of the grass.  There is a grass expert at NCSU, Dr. Fred Yelverton, who might be able to be of better assistance.

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