Our female cat, sadly had to be pts aged 19 and half years just before Christmas, used to love eating grass, I think just for the taste.
She would call you to follow her into the garden then take you to a particular place where she would eat the grass while purring and looking up at you from time to time as if to encourage you to do the same. She clearly enjoyed it.
She never vomited from eating it.
I know that dogs eat different types of grass, wide grass for the taste, other grass for their insides.