> mid-14c., enginour, "constructor of military engines," from Old French engigneor "engineer, architect, maker of war-engines; schemer" (12c.), from Late Latin ingeniare (see engine); general sense of "inventor, designer" is recorded from early 15c.; civil sense, in reference to public works, is recorded from c. 1600 but not the common meaning of the word until 19c (hence lingering distinction as civil engineer). Meaning "locomotive driver" is first attested 1832, American English. A "maker of engines" in ancient Greece was a mekhanopoios.
The original meaning seems to characterize a very specific kind of activity and not what the broad genus "engineer" that we believe today suggests. The growing inclusiveness over time actually seems to suggest that the demarcation between "engineering" and "other arts" is an open question even when posed in historical contexts predating software. The problem of determining whether "software engineering" is engineering is not a problem unique to software development, I think, even putting to one side the numerous cases of what is arguably title puffery.
The ancient Greek "mekhanopoios" is interesting because the ending, "-poios", from "poiesis", refers to making or producing. So the mekhanopoios is someone who produces machines; he does the production. The division of human activity (in relation to knowledge) into poiesis, praxis and theoria seems to give us a good starting point for understanding the myriad activities that human beings engage in because it is a principled classification. But "engineering" seems to have been appropriated for new uses over time for diverse, though not necessarily principled reasons (specialization, analogical similarity, a desire to cash in on established prestige). As a result, at least until the bad appropriations have been dispatched, maybe we cannot expect a crisp taxonomy because the evolution of the meaning of the term has not been principled in the first place.
There does indeed seem to be a connotation of sophistication, specifically scientific sophistication, which is a question of methodology. Even if we accept this definition, sophistication is, of course, a matter of degree, not kind, and what counts as sophisticated seems to be relative to the state of the art. But you could then speak of degrees of engineering. Just as science that is more rigorous and thus more perfect could be said to be more scientific, so, too, we may speak of one field as more of an engineering field than another.
So where does this leave software engineering? If engineering is understood in terms of productive aim achieved by means of scientifically-informed methods, then presumably software is the product, so it's a question of establishing the scientific basis for the field and identifying the "scientifically-informed methods".
[0] https://www.etymonline.com/word/engineer#etymonline_v_25786