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Cosmological inference from weak lensing (WL) surveys is increasingly limited by uncertainties in baryonic physics, which suppress the non-linear matter power spectrum on small scales. Multi-probe analyses that incorporate complementary tracers of the gas distribution around haloes offer a pathway to calibrate these effects and recover unbiased cosmological information. In this work, we forecast the constraining power of a joint analysis combining fiducial data from a Stage-IV WL survey with measurements of the dispersion measure from fast radio bursts (FRBs). We evaluate the ability of this approach to simultaneously constrain cosmological parameters and the astrophysical processes governing baryonic feedback, and we quantify the impact of key FRB systematics, including redshift uncertainties and source clustering. We find that, even after accounting for these effects, a 3×2-point analysis of WL and FRBs significantly improves cosmological constraints, reducing the degradation factor on S8 by ∼80% compared to WL alone. We further show that FRBs alone are sensitive only to a degenerate combination of the key baryonic parameters, log10Mc and ηb, and that the inclusion of WL measurements breaks this degeneracy. Finally, we extend our framework to incorporate galaxy clustering measurements using Luminous Red Galaxy and Emission Line Galaxy samples, performing a unified 6×2-point analysis of WL, dispersion measures of FRBs, and galaxy clustering. While this combined approach tightens constraints on Ωm and log10Mc, it does not lead to a significant improvement in S8 constraints beyond those obtained from WL and FRBs alone.