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We search for additional companions in the GJ 367 exoplanet system, and aim at better constraining its age and evolutionary status. We analyse high contrast direct imaging observations obtained with HST/NICMOS, VLT/NACO, and VLT/SPHERE. We investigate and critically discuss conflicting age indicators based on theoretical isochrones and models for Galactic dynamics. A comparison of GAIA EDR3 parallax and photometric measurements with theoretical isochrones suggest a young age $\le$60 Myr for GJ 367. The star's Galactic kinematics exclude membership to any nearby young moving group or stellar stream. Its highly eccentric Galactic orbit, however, is atypical for a young star. Age estimates considering Galactic dynamical evolution are most consistent with an age of 1 to 8 Gyr. We find no evidence for a significant mid-infrared excess in the WISE bands, suggesting the absence of warm dust in the GJ 367 system. The direct imaging data provide significantly improved detection limits compared to previous studies. At 530 mas (5 au) separation, the SPHERE data achieve a 5 sigma contrast of $2.6 \times 10^{-6}$. The data exclude the presence of a stellar companion at projected separations $\ge$0.4 au. At projected separations $\ge$5 au we can exclude substellar companions with a mass $\ge$ 1.5 M$_{\rm Jup}$ for an age of 50 Myr, and $\ge$ 20 M$_{\rm Jup}$ for an age of 5 Gyr. By applying the stellar parameters corresponding to the 50 Myr isochrone, we derive a bulk density of $ρ_{\rm planet} = 6.2$ g/cm$^3$ for GJ 367b, which is 25% smaller than a previous estimate.