Why are the concepts of short-run and long-run equilibrium exclusive to aggregate supply and demand and macroeconomics? Shouldn’t there also be a concept of short vs. long-run equilibrium in microeconomics? After all, short-run equilibrium describes the state of the economy when wages and prices are still adjusting and when worker misperceptions are affecting quantity-supplied of labor; and long-run equilibrium is the state of the economy when worker misperceptions have been corrected, and wages and prices have adjusted to their final levels. 

Doesn’t this happen in microeconomic situations? If not, why not?
The concepts of short-run and long-run equilibria certainly feature in microeconomics.  Indeed, they have done so for over a century: see Marshall's Principles of Economics (1890).