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Planet-planet scattering events can leave an observable trace of a planet's migration history in the form of orbital misalignment with respect to the the stellar spin axis, which is measurable from spectroscopic timeseries taken during transit. We present high-resolution spectroscopic transits observed with ESPRESSO of the close-in super-Earth $π$ Men c. The system also contains an outer giant planet on a wide, eccentric orbit, recently found to be inclined with respect to the inner planetary orbit. These characteristics are reminiscent of past dynamical interactions. We successfully retrieve the planet-occulted light during transit and find evidence that the orbit of $π$ Men c is moderately misaligned with the stellar spin axis with $λ= -24.0^\circ \pm 4.1^\circ$ ($ψ= 26.9^{\circ +5.8^\circ}_{\,-4.7^\circ}$). This is consistent with the super-Earth $π$ Men c having followed a high-eccentricity migration followed by tidal circularisation, and hints that super-Earths can form at large distances from their star. We also detect clear signatures of solar-like oscillations within our ESPRESSO radial velocity timeseries, where we reach a radial velocity precision of ${\sim}20$ cm/s. We model the oscillations using Gaussian processes and retrieve a frequency of maximum oscillation, $ν_\text{max} = 2771^{+65}_{-60}$ $μ$Hz. These oscillations makes it challenging to detect the Rossiter-McLaughlin effect using traditional methods. We are, however, successful using the reloaded Rossiter-McLaughlin approach. Finally, in an appendix we also present updated physical parameters and ephemerides for $π$ Men c from a Gaussian process transit analysis of the full TESS Cycle 1 data.