Software engineers are in the same class as the people below them - the working class. The entire concept of "middle class" originates from a time when the middle class were non-nobility who were, nonetheless, sufficiently powerful that they needn't worry about things like "keeping their jobs", whether because they were their own employees (as were nearly all doctors, lawyers, etc.) or because they had sufficient social capital not to worry about such trivial things as paid labor.

I want to be clear here: Eton boys were (and are) predominantly middle class, not upper class. In the US, we allowed the idea to be perverted, perhaps because we do not have nobility, and so there is no true "upper class". Given this, the reality is that we are bifurcated into a working class and an owning or capitalist class - though, many would argue (correctly, in my view) that we are in a feudal regime now, rather than a capitalist regime.

To put perhaps too fine a point on it, software engineers are house slaves, and, yes, CEOs and billionaires have done a good job of convincing the field slaves that the house slaves are their enemies, and of convincing house slaves that the field slaves are inferior and just want to take what the house slaves have without working for it.