Interacting dark energy models have been proposed as attractive alternatives to $Lambda$CDM. Forthcoming Stage-IV galaxy clustering surveys will constrain these models, but they require accurate modelling of the galaxy power spectrum multipoles on mildly non-linear scales. In this work we consider a dark scattering model with a simple 1-parameter extension to $w$CDM - adding only $A$, which describes a pure momentum exchange between dark energy and dark matter. We then provide a comprehensive comparison of three approaches of modeling non-linearities, while including the effects of this dark sector coupling. We base our modeling of non-linearities on the two most popular perturbation theory approaches: TNS and EFTofLSS. To test the validity and precision of the modelling, we perform an MCMC analysis using simulated data corresponding to a $Lambda$CDM fiducial cosmology and Stage-IV surveys specifications in two redshift bins, $z=0.5$ and $z=1$. We find the most complex EFTofLSS-based model studied to be better suited at both, describing the mock data up to smaller scales, and extracting the most information. Using this model, we forecast uncertainties on the dark energy equation of state, $w$, and on the interaction parameter, $A$, finding $sigma_w=0.06$ and $sigma_A=1.1$ b/GeV for the analysis at $z=0.5$ and $sigma_w=0.06$ and $sigma_A=2.0$ b/GeV for the analysis at $z=1$. In addition, we show that a false detection of exotic dark energy up to 3$sigma$ would occur should the non-linear modelling be incorrect, demonstrating the importance of the validation stage for accurate interpretation of measurements.
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