Medium-resolution integral-field spectrographs (IFS) coupled with adaptive-optics such as Keck/OSIRIS, VLT/MUSE, or SINFONI are appearing as a new avenue for enhancing the detection and characterization capabilities of young, gas giant exoplanets at large heliocentric distances (>5 au). We analyzed K-band VLT/SINFONI medium-resolution (R_lambda~5577) observations of the young giant exoplanet HIP 65426 b. Our dedicated IFS data analysis toolkit (TExTRIS) optimized the cube building, star registration, and allowed for the extraction of the planet spectrum. A Bayesian inference with the nested sampling algorithm coupled with the self-consistent forward atmospheric models BT-SETTL15 and Exo-REM using the ForMoSA tool yields Teff=1560 +/- 100K, log(g)<4.40dex, [M/H]=0.05 +/- 0.22dex, and an upper limit on the C/O ratio (<0.55). The object is also re-detected with the so-called molecular mapping technique. The technique yields consistent atmospheric parameters, but the loss of the planet pseudo-continuum in the process degrades or modifies the constraints on these parameters. The solar to sub-solar C/O ratio suggests an enrichment by solids at formation if the planet was formed beyond the water snowline (>20 au) by core-accretion. However, a formation by gravitational instability can not be ruled out. The metallicity is compatible with the bulk enrichment of massive Jovian planets from the Bern planet population models. Finally, we measure a radial velocity of 26 +/- 15km/s compatible with our revised measurement on the star. This is the fourth imaged exoplanet for which a radial velocity can be evaluated, illustrating the potential of such observations for assessing the coevolution of imaged systems belonging to star forming regions, such as HIP 65426.
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