Looks about like my lawn looked during a warm rainy spell this last summer.
It should recover with cooler dryer weather. Mine looks a lot better in the last two weeks.
Good reason to go with top-quality seed. If the seed or sod you buy doesn't say resistant to dollarspot--it must be susceptible. I think I overseeded with a seed mix with some low-quality, old-fashioned fine fescue--20 years ago.
I never saw weeds coming out of the center. Dollarspot looks a bit white at first, then turns brown.
It is typical to see many green grass blades with the upper two inches turned white, (and later brown).
On the other hand, necrotic ring spot (summer patch) after a few weeks, often appears in the form of a ring --sometimes with weeds or green grass in the center.
No much commercial experience. In my own lawn, I did not have much success with daconil garden fungicide. No longer labeled for lawns, in any case. The brown spots are gradually recovering. Cool weather now, but still rainy.