Rather does look like a fine upside down chef's hat yet I don't think it's a hat and it's not ceremonial either and generally small bags hold tinder, tobacco, medicine and such. It appears to be a larger sized bag and it's not waterproof to hold liquid. Fascinating choice of material with what looks to be bird foot skin. I'll play on the safe side this time and go with a "gathering storage bag" of sorts and I think it would hold something 'dry'.
I would want to hold it, smell it and look for any remaining visible crumbs inside to identify exactly what it held yet I'd guess that it smells like something gathered from the woods.
@Wayland, thanks for sharing your photos. You must of had quite a bit of fun viewing this fine collection. Cheers.