I mean this very sincerely but I'm a little lost how data engineering is distinct from software engineering. It seems like just a subset of it, my title was software engineer and I've done what sounds like very similar work.

I’m pretty sure the term came from Google (at least that is where I heard it first described) and just referred to a backend engineer with speciality in this area. Now usually these roles have “distributed systems” in the title, even if you aren’t really on the inside of the systems. That or “systems and infrastructure”, “data infrastructure”, or “AI/ML infrastructure” or sometimes “MLE” for those kinds of orgs. Or back to good ole “big data” now that it’s no longer tacked on everything.