When researching veggie "leather", we might also look at bark, leaves etc. and how to make them durable while still pliable.
The idea of layering fibers could go from very simple (pulling sheets of algae out of the water), to very intricate (spinning and weaving flax, nettles). For some, there likely are already good waterproofing techniques.
I'd be interested in very basic approaches, like experimenting with those algae sheets more. After pulling out a sheet of about 1' x 1' it seemed like a fine thing to wrap moss in for diapers, or to use it as a sieve bottom for very fine powder of sorts. Never tried either of these out, though. This topic now made me wonder if you could use wax or such to waterproof it for other uses. It looked promising that the sheet was quite strong and stable as long as it was kept dry.