I read the noun 'state of the art' or the adjective 'state-of-the-art' every now and then, but once in a blue moon I saw 'state of the [non-art]'. I cannot remember what the [non-art]'s are, then I am wondering what the possible idiomatic collocations of 'state of the' would be? And when to use them for what purposes/effects?
The "idiom" you may be thinking of is "State of the Union", an address given by the President of the USA to Congress each year. Many other uses of the phrase consciously or unconsciously follow from this, in that they refer to a detailed report on some significant matter. You may see things titled "A report on the state of the world children" and so on.
State of the art comes from an extension of this sense. It means the current state, in the same way that the State of the Union address is about the current situation of the USA.
It's also common to use "state" in "A state of disorder". A teenager's mum might say "Look at the state of this bedroom" to imply it is very messy and needs to be tidied.
Finally there are expressions like "a state of mind" or "a state of matter". States of mind are "sanity" and "insanity" (etc) and states of matter are gas liquid and solid (etc).