Eppur si muove: Evidence of disc precession or a sub-milliparsec SMBH binary in the QPE-emitting galaxy GSN 069

X-ray quasi-periodic eruptions (QPEs) are intense soft X-ray bursts from the nuclei of nearby low-mass galaxies typically lasting about one hour and repeating every few. Their physical origin remains debated, although so-called impacts models in which a secondary orbiting body pierces through the accretion disc around the primary supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI) system are considered promising. In this work, we study the QPE timing properties of GSN 069, the first galactic nucleus in which QPEs were identified, primarily focusing on Observed minus Calculated (O-C) diagrams. The O-C data in GSN 069 are consistent with a super-orbital modulation on tens of days whose properties do not comply with the impacts model. We suggest that rigid precession of a misaligned accretion disc or, alternatively, the presence of a second SMBH forming a sub-milliparsec binary with the inner EMRI is needed to reconcile the model with the data. In both cases, the quiescent accretion disc emission should also be modulated on similar timescales. Current X-ray monitoring indicates that this might be the case, although a longer baseline of higher-cadence observations is needed to confirm the tentative X-ray flux periodicity on firm statistical grounds. Future dedicated monitoring campaigns will be crucial to test the overall impacts plus modulation model in GSN 069, and to distinguish between the two proposed modulating scenarios. If our interpretation is correct, QPEs in GSN 069 represent the first electromagnetic detection of a short-period EMRI system in an external galaxy, opening the way to future multi-messenger astronomical observations. [abridged]