Engineering is just problem solving with applied scientific knowledge, so it applies to a vast umbrella of disciplines. Your "qualifications" don't actually make a shit, all that matters is if you can do the work. Some of the smartest engineers I've ever met don't have a degree at all, they're just super autistic about their chosen area of expertise.
I don't do software anymore, but it always made me chuckle when people sneered at the "software engineer" moniker, because it is absolutely apt. Anyone who has built or even done a fair amount of work with a codebase of any significant size will tell you just how difficult and challenging it can be.
I work as a systems engineer nowadays and most of it might as well be tee ball in comparison to some of the shit I had to work on as a software engineer. There are certainly challenges, maddening ones even, but it feels like a lazy river in comparison and I'm not working 60-80 hour weeks doing it.