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Let $(V,\omega)$ be an orthosympectic $\mathbb Z_2$-graded vector space andlet $\mathfrak g:=\mathfrak{gosp}(V,\omega)$ denote the Lie superalgebra ofsimilitudes of $(V,\omega)$. When the space $\mathscr P(V)$ of superpolynomialson $V$ is \emph{not} a completely reducible $\mathfrak g$-module, we constructa natural basis $D_\lambda$ of Capelli operators for the algebra of $\mathfrakg$-invariant superpolynomial superdifferential operators on $V$, where theindex set $\mathcal P$ is the set of integer partitions of length at most two.We compute the action of the operators $D_\lambda$ on maximal indecomposablecomponents of $\mathscr P(V)$ explicitly, in terms of Knop-Sahi interpolationpolynomials. Our results show that, unlike the cases where $\mathscr P(V)$ iscompletely reducible, the eigenvalues of a subfamily of the $D_\lambda$ are\emph{not} given by specializing the Knop-Sahi polynomials. Rather, theformulas for these eigenvalues involve suitably regularized forms of thesepolynomials. In addition, we demonstrate a close relationship between oureigenvalue formulas for this subfamily of Capelli operators and theDougall-Ramanujan hypergeometric identity.  We also transcend our results on the eigenvalues of Capelli operators to theDeligne category $\mathsf{Rep}(O_t)$. More precisely, we define categoricalCapelli operators $\{\mathbf D_{t,\lambda}\}_{\lambda\in\mathcal P}^{}$ thatinduce morphisms of indecomposable components of symmetric powers of $\mathsfV_t$, where $\mathsf V_t$ is the generating object of $\mathsf{Rep}(O_t)$. Weobtain formulas for the eigenvalue polynomials associated to the$\left\{\mathbf D_{t,\lambda}\right\}_{\lambda\in\mathcal P}$ that areanalogous to our results for the operators $\{D_\lambda\}_{\lambda\in\mathcalP}^{}$.

Capelli operators for spherical superharmonics and the Dougall-Ramanujan identity