Exploiting KM3NeT/ORCA data to study tau neutrinos and testing the non-unitary mixing matrix

After the measurement of the $\theta_{13}$ mixing angle of the oscillation matrix, neutrino physics entered in its precision era. Validating the 3$\nu$-flavor paradigm through high-precision measurements of the mixing matrix elements is crucial, while exploiting neutrino oscillations to explore physics beyond the Standard Model remains a central focus in neutrino experiments. The water Cherenkov neutrino telescope KM3NeT is under construction in the Mediterranean Sea at two sites: ARCA, offshore Sicily in Italy, and ORCA, offshore Toulon in France. KM3NeT/ORCA is being built to study neutrino oscillations in atmospheric neutrinos traversing the Earth, in the 1-100 GeV energy range. The sensitivity to this energy scale and to effects of matter on the oscillation probabilities enables KM3NeT/ORCA to achieve an early measurement of neutrino mass ordering and to constrain the atmospheric oscillation mixing parameters. Thanks to its huge fiducial mass, KM3NeT/ORCA will collect unprecedented statistics to exploit tau neutrino appearance, enabling an indirect test of the unitarity of the PMNS matrix. In this proceeding, the results of the first unblinded comprehensive study of this detection channel, based on the data collected with a partially instrumented volume (5$\%$ of the nominal), will be presented.