I think the difficulty is the break between job title and discipline. And discipline titles (in all fields) have always been a bit historical-wonky.

By profession, we're all effectively software engineers, data engineers, or computer engineers, according to our work emphasis.

But then you've got the weird break you noted where academically and theoretically, everything we do is math. Or more reasonably, at least a larger proportion than any other discipline except physics and pure math.

So... we could always just go the physics route and retitle the discipline "Computing" and ourselves "Computerists"! (No trailing noun)