Well unless you are getting solid wood utensils (much more $$ and most aren’t) then you are starting with bamboo glued together with adhesives. So at that point if you are worried about the finish I’d be worried about the glues as well
I get solid wood (olive wood or other woods ) tools and I don’t finish them. But if I did I might just use beeswax
They aren’t one piece. See the dark seams? https://www.everythingkitchens.com/totally-bamboo-all-natura...
These are strips glued together aka laminated. The binder is not PVA (which is water soluble and not suitable for the task), it’s most commonly a formaldehyde resin such as phenol- , urea- or melamine urea formaldehyde
That’s plain bambu, the dark areas are the nodes/rings in the plant.
I don’t build cutting boards myself, but have never heard of using anything but food-safe PVA glue. Those resins are used for laminating plywood etc, probably not even legal to use in kitchen utensils, at least in the EU.
Ikea sells solid wood spoons and spatulas starting at like $3.
Cooking utensils are mostly one piece, otherwise wood glue is PVA, same as school glue, that's about as non-toxic as you can get. I'd be more concerned about some kind of supply-chain issue contaminating the raw wood - hopefully they do frequent control checks on the material.