Grass identification is challenging, since nuanced, close-up details are required to be visible to separate similar-looking species. The growth habit we can see in the photos, plus your description of spread, sounds like Bermudagrass.

This is a tenacious and hard-to-eradicate weed, and tips are given in the linked web page. Essentially, your only practical options are to dig it out entirely and replace the sod, or treat colonies of the weed with glyphosate (not all Roundup formulations use this chemical, so check the label). Even so, several repeat treatments with herbicide may be needed before it finally succumbs. Since glyphosate is a non-selective chemical, any desirable turfgrass that the spray contacts will also be damaged or killed, but since this isn't much different than physical removal from the first option (since that can also take away from turfgrass), either way, repair to the lawn may be necessary once you get the Bermudagrass under control.

Miri