I have to disagree. You have a spongy pedal because the size of the bubbles changes with pressure. PV = PV Raise the pressure by a factor of 10, and the volume falls by a factor of 10. Although any gas dissolves more in any liquid as the pressure rises, I doubt brake fluid dissolves much mostly nitrogen air. It has seemed unlikely all along
Tonight, I remembered that years ago I used a pressurized vessel for airless spraying of acrylic lacquer. We first tried CO2 to pressurize the vessel. It made a big mess of things because the CO2 dissolved into the lacquer expanding the volume and thinning the lacquer. When we switched to nitrogen, it solved that problem. N2 is non polar and very little dissolved in the moderately polar lacquer. Even less is going to dissolve in highly polar brake fluid.
I think we need to look at some of the alternative explanations, not air dissolving in brake fluid.