Eco-friendly pouches / small bags?

I'm developing a product with a central value on ecological impact - not just "sustainable", but actually supporting ecological restoration, as a central value integral to the product itself.

The sticking point for me is the bag that holds it. It needs to be about 4" by 3" (approximately), preferably a drawstring bag or other easy access non-zip non-button bag. It should feel high-quality but also be durable.

And, importantly, I need to be able to buy them wholesale with custom logo printing for, say, less than $5 each at large scale.

Organic cotton is widely available but not inspiring to me from an ecological angle. But I haven't found any organic hemp or organic linen or organic bamboo linen or tencel, etc, that is being used to make small bags.

I did find some nice loosely woven sisal bags sold as soap bags, but they're too loose to take a logo. Cork would be ideal for me but I haven't found the right fit.

Anyone have any insights or suggestions, about materials and/or where I might find a supplier?

Thanks 🙏🌿