Are there single words describing the "state of being in a particular shape"? [For Example: "State of being Cylindrical" ]
If you want to express the bloviating verbosity that "X is in the state of being in a cylindrical shape", you simply say that "X is a cylinder" or that "X is cylindrical". Both sentences express the idea that "X is in the state of being in a cylindrical shape", only in 3 or 4 words instead of 11.
Collins has an entry for cylindricity:
Collins proffers a slightly different nuance for the following alternatives:
But, in my opinion, all three words are largely synonymous.
As a generic term for all shapes, you would probably simply use geometry.