Barrow nearly-extensive Gibbs-like entropy favoured by the full dynamical and geometrical data set in cosmology

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 $\mathrm{\Delta }>0.86$, close to the maximum threshold of $\mathrm{\Delta }=1$ 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 ($\mathrm{\Delta }=0$) 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 $\mathrm{\Delta }<0.008$ at the most extreme case.