  We establish a link between open positroid varieties in the Grassmannians
$G(k,n)$ and certain moduli spaces of complexes of vector bundles over Kodaira
cycle $C^n$, using the shifted Poisson structure on the latter moduli spaces
and relating them to the standard Poisson structure on $G(k,n)$. This link
allows us to solve a classification problem for extensions of vector bundles
over $C^n$. Based on this solution we further classify the symplectic leaves of
all positroid varieties in $G(k,n)$ with respect to the standard Poisson
structure. Moreover, we get an explicit description of the moduli stack of
symplectic leaves of $G(k,n)$ with the standard Poisson structure as an open
substack of the stack of vector bundles on $C^n$.
