The Spectral Shovel is crafted within an Infusement Altar. Spectral Shovels are able to dig out a 3x3 area of any Ground type (Sand, Gravel, Dirt, ect).
On release, the Shovel accidentally was able to be enchanted but was later fixed. But due to the bug, there could still be some enchanted spectral stuff out there.
Spectral Tools are not able to be enchanted or repaired. Repairing you will have to use another Spectral but repairing with other items like perfect diamonds is not possible.
In the development of the spectral tools, there was a thought to have the shovel turn into a random shovel between wood and diamond.
Currently, the only way to enchant them, is through villager trades.