Write a function boolean_xnor(a: bool, b: bool) -> bool that takes two boolean inputs, a and b. The function should return the result of the exclusive NOR (XNOR) operation on these inputs. In other words, the function should return True if both inputs are the same (both True or both False), and False otherwise.
For example, if the inputs are True and False, the output should be False because the inputs are different.