I wouldn't eliminate nutsedge from the equation! Both purple (Cyperus rotundus) and yellow (Cyperus esculentus) nut sedge produce underground rhizomes that help with their spread. Purple nutsedge in particular will form long networks of rhizomes. "The rhizomes remove nutrients from the soil robbing their fellow plants and can be very difficult to remove. If you pull it up you can see the nut-like nodules that store the nutrients (and are edible) as well as a network of long roots. Unfortunately, once pulled up, the Nutsedge may leave broken roots to form more numerous roots and therefore, new plants in its place "

Identification is critical as nutsedge does not respond to regular herbicides and even the two species require different approaches in their control. Nutsedges can be distinguished from grasses by their stems, which are triangular or V-shaped in cross-section, while grass stems are hollow and round. Their leaves are thicker and stiffer than most grasses and are arranged in groups of three at the base. Nutsedge leaves appear creased with prominent mid-veins.

I Cyperus esculentus has rhyzomes, but Ive never seen it spread by rhzomes It's considered native to NA, as well as Europe. There is a variety/subpecies that originates from southern Europe that may be the aggresive nutsedge in American gardens. This nutsedge is a conspicuous bright, light greenish/yellow when it 1st emerges. This sedge isn't a pest in the wild, but can be horrible in gardens and yards where there is bare soil and disturbed areas. Correction: it Does have rhizomes, but Ive never seen them spreading by rhyzomes. They spread because of all the little nutlets that remain in the soil after they are pulled out. Probably better to dig them out with the soil they are occupying?

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4373285/#:~:text=Cyperus%20esculentus%20var.,et%20al.%2C%201995). .

https://www.illinoiswildflowers.info/grasses/plants/yn_sedge.htm#:~:text=Yellow%20Nut%20Sedge%20(Cyperus%20esculentus)&text=Description%3A%20This%20perennial%20sedge%20is,the%20base%20of%20the%20plant

" Yellow nutsedge is a perennial plant growing from an extensive system of rhizomes, tubers and roots, with stems reaching 12 to 32 inches tall. With age, its rhizomes develop tubers and basal bulbs that bear aerial shoots. " WA State Noxious Weeds

" Yellow nutsedge is a grass-like weed in the sedge family (Cyperaceae) with top growth 8–30 inches tall (Fig. 1a), and an extensive underground network of basal bulbs, roots, thin fibrous rhizomes, and tubers 0.4–0.8 inch long borne singly at the tips of rhizomes (Uva et al., 1997; Holm et al., 1991)." eOrganic

" Nutsedge is a perennial weed. Perennial weeds are always more difficult to control. But, nutsedge is one of the toughest because it spreads by underground rhizomes and tubers. Four to six weeks after the first blades emerge, typically in late June to early July, nutsedge begins forming new tubers (nutlets) and rhizomes (underground stems)." Clackamas Conservation District

" Yellow Nutsedge, is a perennial, glossy green, grass-like native weed or sedge that spreads predominantly by rhizomes and tubers, although viable seed can be produced. " NC Extension

Cyperus rotundus doesn't occur in Illinois, so don't have experience with it. I always remove C. esculentes

before the rhizomes have a chance to spread.

Cyperus esculentes

Cyperus rotundus

The OP photo does look a lot like Bermuda grass, tho...

Bermuda grass. The common one, not the improved varieties. Pest. It can climb under, over, and through anything. The least little piece left will root.

Makes a sturdy grass for lawns, but invades flower beds.