  The phenomenon of quantum superposition manifests in two distinct ways: it
either spreads out across non-orthogonal basis states or remains concealed
within their overlaps. Despite its profound implications, the resource theory
of superposition often neglects the quantum superposition residing within these
overlaps. However, this component is intricately linked to a form of state
indistinguishability and can give rise to quantum correlations. In this paper,
we introduce a pseudo-Hermitian representation of the density operator, wherein
its diagonal elements correspond to biorthogonal extensions of Kirkwood-Dirac
quasi-probabilities. This representation provides a unified framework for the
inter-basis quantum superposition and basis state indistinguishability, giving
rise to what we term as \textit{genuine} quantum superposition. Moreover, we
propose appropriate generalizations of current superposition measures to
quantify genuine quantum superposition that serves as the fundamental notion of
nonclassicality from which both quantum coherence and correlations emerge.
Finally, we explore potential applications of our theoretical framework,
particularly in the quantification of electron delocalization in chemical
bonding and aromaticity.
