Catalytic microswimmers convert the chemical energy of a fuel into motion, sustaining spatial chemical gradients and fluid flows that drive their propulsion. This leads to unconventional individual behavior and the emergence of collective dynamics, absent in equilibrium. The characterization of the nonequilibrium interactions driven by those concentration gradients and flows around microswimmers is challenging owing to the importance of fluctuations at the microscale. Previous experiments have focused on large Janus microspheres attached to a surface, and did not investigate non-equilibrium interactions for freely moving microswimmers of various shapes. Here we show a massive dependence of the non-equilibrium interactions on the shape of small catalytic microswimmers. We perform tracking experiments at high troughput to map non-equilibrium interactions between swimmers and colloidal tracers in 2D, accurate down to tracer velocity of 100nm/s. In addition, we devise a novel experimental method combining two types of tracers with differing phoretic mobility to disentangle phoretic interactions in concentration gradients from hydrodynamic flows. We benchmark the method with experiments on a single chemically active site and on a catalytic microswimmer tethered to a surface. We further investigate the activity-driven interactions of freely moving catalytic dimers as microswimmers, for a wide range of aspect ratio between the active and passive part. We confront our results with standard theoretical models of microswimmers near surfaces and show poor agreement, ruling out phoresis as the main interaction for catalytic swimmers. Our findings provide robust quantitative measurements of the non-equilibrium interactions of catalytic microswimmers of various geometry with their environment. The work notably indicates the need for theoretical development, and lays the groundwork for the quantitative description of collective behavior in suspensions of phoretically-driven colloidal suspensions.