Most likely suckers from root stock.

To my horror almost the same thing happed to me with the exact same weed. My weed issue started when I discovered what I believe to be patches of Annual Blue grass. From what I can tell the Annual Blue grass is seeding itself now because it will die once it gets hot, and return in the fall. So pre emergent needs to happen in late August beginning of September. I couldn't locate anything that would kill it, I read that its mostly controlled with pre emergent. It was in so few places I just started to pull it by hand. Then the weeds in your picture started showing up everywhere, and I mean everywhere. I've tried searching google images, the only one I see that resembles it is barnyard grass

Or you could just watch it more closely and trim it back as needed.... We don't "nuke" stuff at my house. Be mindful of the environment please. Ground cover will typically spread out pretty aggressively. That is a double edged sword. Watch it and trim/coax it in the right direction and it will be what you need. Let runners take root everywhere and vines climb over your ornamentals, and then you have a problem. Morning Glories, Phlox, Mint, Blackberries, good ol choke vine, all of these and more will spread out and kill everything they touch so they can grow on the rotting corpse. That is aggressive. Do not be afraid to be aggressive with your trimming and pruning. What type of ground cover are you talking about? If you don't have time, patience, or energy to keep it in check, maybe you should rip it all out (get the roots or it will come back) and just spread a visually pleasing mulch around your flower beds.

Euphorbia prostrata or maculata. An annual. If you do nothing, the existing plants will be killed over winter, but more will sprout next year. Stopping the cycle of letting new seeds drop will drastically reduce their numbers in future years. You can pour boiling water on your path to kill unwanted plants (including the roots if they get hot enough) but that may not render all of the existing seeds unable to sprout. Pulling what you have now, since the plants are so big, then treating with BW as needed should keep the path more clear. The cracks between the bricks are deep. That's allowing many seeds to become lodged in there. Filling/packing the cracks tightly again should help prevent many seeds from being able to get stuck there. There is rough sand sold just for this purpose.