Which web does the SNAP get the auxiliary data for atmospheric correction?

The influence on the result of the four parameters is quite different. So, the need to provide the values is different. Following some comments on the parameters.

Ozone: The sensitivity to ozone is quite significant. The resulting water leaving reflectance spectra varies particularly in the blue. The good news is that there are good observations from satellite, and also model predications are as good as needed for AC over ocean.
For MERIS and OLCI, ozone is taken from ECMWF data contained in the products. Since January 2022 ECMWF data is also available in S2 products in SNAP. The C2RCC processor needs an update to make use of the newly available data.

Salinity and Sea Surface Temperature: Those parameters need to be considered in combination. The impact of salinity and temperature on the pure water absorption was subject of a project some years ago. The result of this project was an update of Case2Regional with temperature and salinity as additional input neurons of the neural nets.

The influence of temperature in itself is negligible overall. The influence of salinity is relevant at low temperature, and then only the extremes matter. I.e., it makes a difference if we are in open ocean (S=36) or fresh water (S=0). In oceanic waters salinity varies between 34 and 36 (somehow) and this doesn’t matter.

The Baltic Sea in winter may be relevant. Here salinity varies between ~0 in the Neva Bay and S~25 in the Western Baltic.

Air Pressure: The air pressure has a very large impact. It is the measure of air molecules in the path of light, and thus it is determining the Rayleigh scattering, which contributes 90% or more of the signal measured at the satellite, wavelength dependent. Small errors in air pressure lead to large errors in the water reflectance and thus to errors in the IOPs and concentration values.