Not sure if it is annua. Do you have a lawn mixture with supina? You won’t get rid of it by mowing. Annua and also supina love a deep cut. The lawn does not die. Glyphosate on it and overseed the next day. Or dig it out. Or just overseed the rest of the lawn now and then with a lighter mixture. Then it won’t be noticeable anymore. Some PGA golf courses rely on Annua. With regular mowing (with sharp blades), fertilizer, and water, you achieve 80-90%. If you want more, it becomes (as almost always) significantly more labor-intensive.