It’s actually possible to make paper from a wide variety of things. Humans have been making paper, or things like paper for a very long time -two thousand years or so. Paper originally was made of old rags, not wood pulp.
Making paper by hand is perfectly doable, if a bit tedious. The process is essentially the same, no matter the material. Dry, cut, cook (simmer, really), blend, and then use a screen to pull out some of the paper pulp. Dry.
The cooking process is done to break down the fibers, often with chemical assistance. That said, it isn’t strictly necessary, though chemical additives might reduces the blending time. Blending thoroughly is important.
It doesn’t have to be pure grass clippings- in fact, for the first time making paper, recycling old paper scraps is the easiest. That said, paper making seems to be possible with most forms of fibers- I once had students do so with packing peanuts.
Air drying generally works fine, though modern paper mills will use heat of some sort for the drying. Homemade paper doesn’t have the additives that make it shiny, easy to write on, or long lasting. It also typically lacks the clay that can be used to make a firmer paper.
I’ll admit that paper making falls into the category of things I classify as both neat, and not worth the effort of doing a second time.