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Modern weak-lensing observations are becoming increasingly sensitive tobaryonic feedback processes which are still poorly understood. So far, thischallenge has been faced either by imposing scale-cuts in the data or bymodelling baryonic effects with simple, one-parameter models. In this paper, werely on a more general, seven-parameter prescription of baryonic feedbackeffects, which is primarily motivated by observations and has been shown toagree with a plethora of hydrodynamical simulations. By combining weak-lensingdata from the Kilo-Degree Survey (KiDS-1000) with observations of gas aroundgalaxy clusters, we are able to constrain baryonic parameters and learn moreabout feedback and cosmology. In particular, we use cluster gas fractions fromX-ray data and gas profiles from kinematic Sunyaev-Zeldovich (kSZ) observationsto provide evidence for baryonic feedback that is stronger than predicted bymost hydrodynamical simulations. In terms of the matter power spectrum, wereport a beyond-percent effect at wave-modes above $k\sim 0.1-0.45$ h/Mpc and amaximum suppression of $12-33$ percent at $k\sim7$ h/Mpc (68 percent confidencelevel). Regarding the combined parameter$\Sigma_8=\sigma_8(\Omega_m/0.3)^{0.58}$, we find the known tension with thePlanck satellite data to be reduced from 3.8 to 2.9 $\sigma$ once baryoniceffects are fully included in the analysis pipeline. The tension is furtherdecreased to 2.6 $\sigma$ when the weak-lensing data is combined with X-ray andkSZ observations. We conclude that, while baryonic feedback effects become moreimportant in modern weak-lensing surveys, they are unlikely to act as the mainculprit for the observed $\Sigma_8$-tension.

Constraining baryonic feedback and cosmology with weak-lensing, X-ray, and kinematic Sunyaev-Zeldovich observations