Cohomology of twisted polynomial superfunctors through the twisting spectral sequence

We want to compute generic $\mathrm{E}\mathrm{x}\mathrm{t}$-spaces of twisted polynomial functors in relation to the $\mathrm{E}\mathrm{x}\mathrm{t}$-spaces of the untwisted ones, modulo a parametrisation. Thanks to the study of a spectral sequence we get to a computation in low degrees, with remarkable consequences at the level of generic cohomology.