I've made sheaths from wood. A strong tight-grained wood is best. I've used maple, a particularly hard yellow pine, and bamboo. Cut two pieces to the blade outline plus a margin, use a gouge to hollow the insides (the bamboo was pretty much hollow enough), gluing it together can add strength and definitely makes lashing easier, apply lashings. The lashing at the top has to be more substantial and you need one low to keep the blade from splitting the sheath low. You can add as many lashings as you want.

Lashings can be any stout cord. I've used black nylon mason line and copper wire. Leather strips would work and can be shrunk in place as long as you don't crush the wood. Any extra lashings or windings can be used for survival uses. Just be sure to separate the stored materials from the ones holding the sheath together.

Amenities that could be considered are to soak the wood in oil, or use a naturally oily wood, a sheath made of lightered wood would mean you always have tinder. Boring small holes low would allow water to drain and might be arranged to allow a thong to be easily attached to keep it from slapping around.

Wood can be bonded or impregnated with epoxy or other resin and reinforced with various fabrics.

Ive seen a demonstration of a guy grease a knife blade with mold release compound and wrap the blade in polyester mesh soaked in resin and follow with several layers of fiberglass run flat across the blade. This keeps the glass away from the edge so it doesn't wear the edge. I forget the details. Might have been Kevlar and vinylester. He strapped the blade down to a piece of plastic and worked one side at a time after the initial wrap and let mats run wild three or four inches on either side. With the mats soaked beforehand the process took a few minutes. Once hardened overnight he cut it to the final shape but left tabs to allow lashing points.

In a book I read they said some people would dip their blade on molten zinc or lead and this provided a nice tight fit. No work on how dipping your carefully heat treated blade in molten metal.

I have also seen sheaths made out of sheet brass or copper. One impressed me with brass tubing slit and brazed around the blade outline so the edge never touches the brass.

I'm more a wood kind of guy.

Lots of options. For more ideas look into historic knife and sword sheaths.