That's a very astute observation. From a synoptics standpoint, warmer sea surface temperatures are generally associated with lower pressures due to convective tendencies and rising air. Without getting into too much details: (1) warmer SSTs means (2) increased diabatic heating of the air above which leads to (3) air is less dense and rises and (4) this lowers pressure at the surface. Conversely, cooler SSTs tend to coincide with higher pressure (due to sinking air/subsidence).
There is a caveat here though, this mostly occurs at the surface or lower levels. We'd need to further analyze geopotential heights at 500mb (I've plotted these below for every seasonal model available at Copernicus), which is influenced more by atmospheric pressure patterns (i.e., large-scale atmospheric circulation features like jet streams, planetary waves, and Rossby waves). We'd also need to look at wind data, which I'll plot at another time, but from the geopotential height plots, I would say yes.
![Image](https://i.imgur.com/MUIgqD3.jpeg)