Don't ask me why I take my cat for walks outside. When she was a kitten, it seemed like a good idea.... now she's waiting by the door all the time.
Cat walking is not like dog walking. My neighbors dogs trot along obediently. I wave from my yard. I'm just standing there like an idiot while my cat takes a nap in the grass. Or decides to zip after a butterfly so I get yanked along for the ride. Or digging up mole holes so she has muddy paws when we get inside.
Cat's have no concept of path and no incentive to go in one direction. A bug will set off a mad rush into the tall grass, followed by several minutes of grass chewing, followed by another mad rush after another bug, followed by a roll-over and take-a-break moment.
On and on it goes, as we wander down the path to the field below. My cat is an 'down-hill' traveler, which means when it's time to go home, I'm carrying a 15 pound cat uphill all the way.
However, when I'm outside on 'cat time', with nothing else to do but wait around, I have an opportunity to pay attention to what is growing. And what a variety there is!
I was able to identify this grass with tassels as 'sedge' . Turns out it's similar to the tall ornamental grasses all over the neighborhood, and supposedly has edible tubers. If the cat slows down at some point, I will dig one up and see.