  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.
