  We apply the full set of most update dynamical and geometrical data in
cosmology to the nonextensive Barrow entropic holographic dark energy. We show
that the data point towards an extensive Gibbs-like entropic behaviour for the
cosmological horizons, which is the extreme case of the Barrow entropy, with
the entropy parameter being $\Delta > 0.86$, close to the maximum threshold of
$\Delta =1$ where the fractal dimension of the area-horizon becomes almost or
just the volume and the intensivity is recovered. Futhermore, we find that the
standard Bekenstein area-entropy limit ($\Delta = 0$) is excluded by the set of
our data. This contradicts the bounds obtained recently from early universe
tests such as the baryon asymmetry, the big-bang nucleosynthesis, and the
inflation limiting $\Delta< 0.008$ at the most extreme case.
