A regular shulker box, when put into a smithing table (just like any other tool) along with a netherite ingot will convert it into a netherite shulker box (previous enchantments, items and name will remain, but the dye will be removed).

Enchantments can be added to this shulker box just like a regular one.

Texture-:
The box will have a texture similar to the netherite block, but more rugged.
The bottom texture, opposing the side it is opened from, will have a texture/colour similar to ancient debris, but more refined and slightly darker

Sound-:
It could make a kind of distorted sound that a regular shulker makes when opened, but mixed with some nether vibes

Advantage/Feature of this box-:
It won't burn in lava or fire and it will retain all items (until it despawns)

Disadvantages over regular shulker box-:
Takes longer time to break
Requires an iron pickaxe or better to break
Cannot be dyed
Cannot be changed back to regular shulker box

This feature request was inspired from a comment in Xisuma's mod showcase video by "BrickBot 2.0"

If a "netherite shulker box" was broken without a pickaxe, or with a wooden or stone pickaxe, would the shulker box drop its contents or delete its contents? I would prefer the former over the latter.

I agree, dropping the contents makes more sense.

If a "netherite shulker box" was broken without a pickaxe, or with a wooden or stone pickaxe, would the shulker box drop its contents or delete its contents? I would prefer the former over the latter.