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Explaining the existence of $\gtrsim10^8\,\mathrm{M_\odot}$ SMBHs at $z>6$ is a persistent challenge to modern astrophysics. Multi-wavelength observations of $z\gtrsim6$ QSOs reveal that, on average, their accretion physics is similar to that of their counterparts at lower redshift. However, QSOs showing properties that deviate from the general behavior can provide useful insights into the physical processes responsible for the rapid growth of SMBHs in the early universe. We present X-ray (XMM-Newton, 100 ks) follow-up observations of a $z\approx6$ QSO, J1641+3755, which was found to be remarkably X-ray bright in a 2018 Chandra dataset. J1641+3755 is not detected in the 2021 XMM-Newton observation, implying that its X-ray flux decreased by a factor $\gtrsim7$ on a notably short timescale (i.e., $\approx115$ rest-frame days), making it the $z>4$ QSO with the largest variability amplitude. We also obtained rest-frame UV spectroscopic and photometric data with textit{LBT}, and compared them with archival datasets. Surprisingly, we found that J1641+3755 became brighter in the rest-frame UV band from 2003 to 2016, while no strong variation occurred from 2016 to 2021. Multiple narrow absorption features are detected in its rest-frame UV spectrum, and several of them can be associated with an intervening system at $z=5.67$. The variability properties of J1641+3755 can be due to intrinsic variations of the accretion rate, a small-scale obscuration event, gravitational lensing due to an intervening object, or an unrelated X-ray transient in a foreground galaxy in 2018. Accounting for all of the $z>6$ QSOs with multiple X-ray observations separated by $>10$ rest-frame days, we found an enhancement of strongly (i.e., by a factor $>3$) X-ray variable objects compared to QSOs at later cosmic times. This finding may be related to the physics of fast accretion in high-redshift QSOs.