Stellar variability strongly impacts the search for low-mass exoplanets with radial velocity techniques. Two types of planet-free time series can be used to quantify this impact: models and direct solar observations after a subtraction of the Solar System planetary contribution. Making a comparison among these approaches is necessary to improve the models, which can then be used for blind tests across a broad range of conditions. Our objective is therefore to validate the amplitude of the convective blueshift in plages used in our previous works, particularly in blind tests, with HARPS-N solar data. We applied our model to the structures observed at the time of HARPS-N observations and established a direct comparison between the radial velocity time series. To complete our diagnosis, we also studied the observed radial velocities separately for each diffraction order derived from the individual cross-correlation functions, as well as our line-by-line radial velocities. We find that our previous model had been underestimating the amplitude of the convective blueshift inhibition by a factor of about 2. A direct estimation of the convective blueshift in the spectra, which is shown to be correlated with the plage filling factor, allows us to explain the difference with previous estimations obtained with MDI/SOHO Dopplergrams, based on the specific properties of the Ni line used in this mission. In addition, we identified several instrumental systematics, in particular, the presence of a 2m/s peak-to-peak signal with a period of about 200 days in radial velocity and bisector. This signal could be due to periodic detector warmups, a systematic dependence of the long-term trend on wavelength that is possibly related to the variability of the continuum over time, and/or an offset in radial velocity after the interruption of several months in October 2017. A large amplitude in the convective blueshift inhibition of (360m/s, namely twice more than in our previous works) must be used when building synthetic times series for blind tests. The presence of instrumental systematics should also be taken into account when using sophisticated methods based on line properties to mitigate stellar activity when searching for very weak signals.