Symplectic leaves in projective spaces of bundle extensions

Fix a stable degree-n rank-k bundle $F$ on a complex elliptic curve for (coprime) $1\le k<n\ge 3$. We identify the symplectic leaves of the Poisson structure introduced independently by Polishchuk and Feigin-Odesskii on $P^{n-1}\cong P{\mathrm{Ext}}^1(F,O)$ as precisely the loci classifying extensions $0\to O\to E\to F\to 0$ with $E$ fitting into a fixed isomorphism class, verifying a claim of Feigin-Odesskii. We also classify the bundles $E$ which do fit into such extensions in geometric/combinatorial terms, involving their Harder-Narasimhan polygons introduced by Shatz.