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We present a detailed follow-up of the very energetic GRB 210905A at a high redshift of z = 6.312 and its luminous X-ray and optical afterglow. We obtained a photometric and spectroscopic follow-up in the optical and near-infrared (NIR), covering both the prompt and afterglow emission from a few minutes up to 20 Ms after burst. With an isotropic gamma-ray energy release of Eiso = 1.27E54 erg, GRB 210905A lies in the top ~7% of gamma-ray bursts (GRBs) in terms of energy released. Its afterglow is among the most luminous ever observed. It starts with a shallow evolution that can be explained by energy injection, and it is followed by a steeper decay, while the spectral energy distribution is in agreement with slow cooling in a constant-density environment within the standard fireball theory. A jet break at ~ 46.2+-16.3 d (~6.3 d rest-frame) has been observed in the X-ray light curve; however, it is hidden in the H band due to the contribution from the likely host galaxy, the fourth GRB host at z > 6 known to date. We derived a half-opening angle of 8.4+-1.0 degrees, which is the highest ever measured for a z>6 burst, but within the range covered by closer events. The resulting collimation-corrected gamma-ray energy release of 1E52 erg is also among the highest ever measured. The moderately large half-opening angle argues against recent claims of an inverse dependence of the half-opening angle on the redshift. The total jet energy is likely too large to be sustained by a standard magnetar, and it suggests that the central engine of this burst was a newly formed black hole. Despite the outstanding energetics and luminosity of both GRB 210905A and its afterglow, we demonstrate that they are consistent with those of less distant bursts, indicating that the powering mechanisms and progenitors do not evolve significantly with redshift.