Modern weak-lensing observations are becoming increasingly sensitive to baryonic feedback processes which are still poorly understood. So far, this challenge has been faced either by imposing scale-cuts in the data or by modelling baryonic effects with simple, one-parameter models. In this paper, we rely on a more general, seven-parameter prescription of baryonic feedback effects, which is primarily motivated by observations and has been shown to agree with a plethora of hydrodynamical simulations. By combining weak-lensing data from the Kilo-Degree Survey (KiDS-1000) with observations of gas around galaxy clusters, we are able to constrain baryonic parameters and learn more about feedback and cosmology. In particular, we use cluster gas fractions from X-ray data and gas profiles from kinematic Sunyaev-Zeldovich (kSZ) observations to provide evidence for baryonic feedback that is stronger than predicted by most hydrodynamical simulations. In terms of the matter power spectrum, we report a beyond-percent effect at wave-modes above k ~ 0.1-0.45 h Mpc^-1 and a maximum suppression of 12-33 per cent at k ~ 7 h Mpc^-1 (68 per cent confidence level). Regarding the combined parameter Σ₈ = σ₈(Ω_m/0.3)^0.58, we find the known tension with the Planck satellite data to be reduced from 3.8 to 2.9 σ once baryonic effects are fully included in the analysis pipeline. The tension is further decreased to 2.6 σ when the weak-lensing data is combined with X-ray and kSZ observations. We conclude that, while baryonic feedback effects become more important in modern weak-lensing surveys, they are unlikely to act as the main culprit for the observed Σ₈-tension.