The HARPS-N solar telescope has been observing the Sun every possible day since the summer of 2015. We recently released 10 years of these data, which are available online.The goal of this manuscript is to present the different optimisations made to the ESPRESSO data reduction software used to extract the published HARPS-N solar spectra, to describe data curation, and to perform some analyses that demonstrate the extreme RV precision of those data. By analysing all the HARPS-N wavelength solutions over 13 years, we bring to light instrumental systematics at the 1ms level. We mitigate those systematics by curating the thorium line list used to derive the wavelength solution, and by applying a correction to the drift of thorium lines induced by the aging of thorium-argon hollow cathode lamps. After optimisation, we demonstrate a peak-to-peak precision on the HARPS-N wavelength solution better than 0.75ms over 13 years. We then carefully curate the decade of HARPS-N re-reduced solar observations by rejecting 30% of the data affected either by clouds, bad atmospheric conditions} or well-understood instrumental systematics. Finally, we correct the curated data for spurious sub-\ms RV effects caused by erroneous instrumental drift measurements and by changes in the spectral blaze function over time. After curation and correction, a total of 109466 HARPS-N solar spectra and respective RVs over a decade are available. The median photon-noise precision of the RV data is 0.28ms and, on daily timescales, the median RV rms is 0.49ms, similar to the level imposed by stellar granulation signals. On 10-year timescales, the large RV rms of 2.95\ms results from the RV signature of the Sun's magnetic cycle. When modeling this long-term effect using the Bremen Composite Magnesium II activity index, we demonstrate a long-term RV precision of 0.41ms. We also analysed contemporaneous HARPS-N and NEID solar RVs and found the data from both instruments to be of similar quality and precision. However, an analysis of the RV difference between these two RV datasets over the three available years gives a surprisingly large RV rms of 1.3ms. This variation is dominated by an unexplained trend that could be caused by a different sensitivity to stellar activity of the two datasets. Once this trend is modeled, the overall RV rms for three years reaches 0.79ms, and the RV rms during the low activity phase decreases to 0.6ms, compatible with what is expected from supergranulation. This decade of high-cadence HARPS-N solar observations with short- and long-term precision below 1ms represents a crucial dataset for further understanding stellar activity signals in solar-type stars and to advance other science cases requiring such extreme precision.