At low redshift, a handful of gamma-ray bursts (GRBs) have been discovered with peak luminosities ($L_{rm iso} < 10^{48.5}~rm{erg,s}^{-1}$) substantially lower than the average of the more distant ones ($L_{rm iso} > 10^{49.5}~rm{erg,s}^{-1}$). The properties of several low-luminosity (low-$L$) GRBs indicate that they can be due to shock break-out, as opposed to the emission from ultrarelativistic jets. Owing to this, it is highly debated how both populations are connected, and whether there is a continuum between them. The burst at redshift $z=0.283$ from 2012 April 22 is one of the very few examples of intermediate-$L$ GRBs with a $gamma$-ray luminosity of $Lsim10^{48.9}~rm{erg,s}^{-1}$ that have been detected up to now. Together with the robust detection of its accompanying supernova SN 2012bz, it has the potential to answer important questions on the origin of low- and high-$L$ GRBs and the GRB-SN connection. We carried out a spectroscopy campaign using medium- and low-resolution spectrographs at 6--10-m class telescopes, covering the time span of 37.3 days, and a multi-wavelength imaging campaign from radio to X-ray energies over a duration of $sim270$ days. Furthermore, we used a tuneable filter centred at H$alpha$ to map star formation in the host galaxy and the surrounding galaxies. We used these data to extract and model the properties of different radiation components and incorporate spectral-energy-distribution fitting techniques to extract the properties of the host galaxy. Modelling the light curve and spectral energy distribution from the radio to the X-rays revealed the blast-wave to expand with an initial Lorentz factor of $Gamma_0sim60$, low for a high-$L$ GRB, and that the afterglow had an exceptional low peak luminosity-density of $lesssim2times10^{30}~rm{erg,s}^{-1},rm{Hz}^{-1}$ in the sub-mm. [Abridged]
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