arXiv:2611.13467v1 Announce Type: new Abstract: This paper investigates the weak convergence of a fully discrete approximation for a class of semilinear stochastic partial differential equations (SPDEs) driven by multiplicative Gaussian and Poisson noise. The scheme combines a spectral Galerkin discretization in space with an exponential Euler discretization in time. Compared with single-noise settings, the simultaneous presence of continuous and jump perturbations introduces additional challenges arising from discontinuous trajectories, nonlocal jump operators, and their interaction with state-dependent multiplicative coefficients. To overcome these difficulties, we establish the exponential integrability of the numerical solution processes and refined moment estimates in negative Sobolev norms for the associated first- and second-order variational processes. Combining these estimates with a discrete-time approximation argument and Wiener--Poisson Malliavin calculus, we derive regularity estimates for the solutions of the Kolmogorov equations associated with the spatial Galerkin approximations. Based on these estimates, we obtain the temporal and spatial weak convergence orders arbitrarily close to one with respect to discretization parameters $\tau$ and $\lambda_N^{-1}$, respectively. To the best of our knowledge, this provides the first weak convergence result for a fully discrete approximation of semilinear SPDEs with simultaneous multiplicative Gaussian and Poisson noise.