What is the range of horizontal pressure gradients typically caused by the differential heating of land and water under sea breeze conditions?
In his book, Simpson (Simpson, J. E. (1994). Sea breeze and local winds. Cambridge University Press) shows a figure that includes the pressure difference between Jersey in the Channel Islands and Paris. It gives an idea of the magnitude of the pressure difference. As was mentioned in the comments, sea breeze tends to be perceived as a density current on constant pressure surfaces.