The multifaceted central radio galaxy of the cluster RBS 797 shows several episodes of jet activity in multiple directions. We wish to understand the causes behind these dramatic misalignments and measure the timescales of the successive outbursts. We present a multifrequency (144 MHz -- 9 GHz) and multiscale (5 pc -- $50$ kpc) investigation of the central radio galaxy in RBS 797, by means of JVLA, LOFAR (with international stations), e-Merlin, VLBA, and EVN data. We investigate the morphological and spectral properties of the radio lobes, the jets, and the active core. We confirm the co-spatiality of the radio lobes with the four perpendicular X-ray cavities previously discovered. The radiative ages of the east-west lobes ($31.4 Myr) and of the north-south lobes ($32.1 Myr) support a coeval origin of the perpendicular outbursts, which also have similar active phase duration (sim 12 Myr). Based on the analysis of the inner north-south jets (on scales of $ kpc), we (a) confirm the S-shaped jet morphology; (b) show the presence of two hotspots per jet with a similar spectral index; and (c) estimate the age of the twisting north-south jets to be less than $ Myr. Based on these results, we determine that jet precession, with a period sim 9 Myr, half-opening angle sim circ $, and jet advance speed sim 0.01$c$, can explain the properties of the north-south jets. We also find that the synchrotron injection index has steepened from the large, older outbursts ($ to the younger S-shaped jets ($ possibly due to a transition from FR I-like to FR II-like activity. The e-Merlin, VLBA, and EVN data reveal a single, compact core at the heart of RBS 797, surrounded by extended radio emission whose orientation depends on the spatial scale sampled by the data. We explore several engine-based scenarios to explain these results. Piecing together the available evidence, we argue that RBS 797 likely hosts (or hosted) binary active supermassive black holes (SMBHs). The detection of a single component in the VLBA and EVN data is still consistent with this interpretation, since the predicted separation of the binary SMBHs (leq 0.6 pc) is an order of magnitude smaller than the resolution of the available radio data (5 pc).
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