Euclid preparation. LII. Forecast impact of super-sample covariance on 3x2pt analysis with Euclid

Deviations from Gaussianity in the distribution of the fields probed by large-scale structure surveys generate additional terms in the data covariance matrix, increasing the uncertainties in the measurement of the cosmological parameters. Super-sample covariance (SSC) is among the largest of these non-Gaussian contributions, with the potential to significantly degrade constraints on some of the parameters of the cosmological model under study -- especially for weak-lensing cosmic shear. We compute and validate the impact of SSC on the forecast uncertainties on the cosmological parameters for the photometric survey, and investigate how its impact depends on the specific details of the forecast. We followed the recipes outlined by the Euclid Collaboration (EC) to produce $1 constraints through a Fisher matrix analysis, considering the Gaussian covariance alone and adding the SSC term, which is computed through the public code PySSC . The constraints are produced both by using photometric probes in isolation and by combining them in the `3times 2pt' analysis. We meet EC requirements on the forecasts validation, with an agreement at the 10 level between the mean results of the two pipelines considered, and find the SSC impact to be non-negligible -- halving the figure of merit (FoM) of the dark energy parameters ($w_0$, $w_a$) in the 3times 2pt case and substantially increasing the uncertainties on $ m w_0$, and $ for the weak-lensing probe. We find photometric galaxy clustering to be less affected as a consequence of the lower probe response. The relative impact of SSC, while highly dependent on the number and type of nuisance parameters varied in the analysis, does not show significant changes under variations of the redshift binning scheme . Finally, we explore how the use of prior information on the shear and galaxy bias changes the impact of SSC. We find that improving shear bias priors has no significant influence, while galaxy bias must be calibrated to a subpercent level in order to increase the FoM by the large amount needed to achieve the value when SSC is not included.