I really don't get the point of gatekeeping a job title.
There's no official license or certification for software engineering in the US, so anyone claiming you have to meet some requirement to call yourself a software engineer is factually wrong. Now, pretty much every tech company calls anyone who writes code some form of engineer, so much so that SDE/SWE is a pretty universal acronym.
I really don't care personally, and I don't go around grouping myself in with other engineering fields. But for the past 7 or so years, my actual job title has had the word "engineer" in it despite the fact that I don't have a Bachelor's degree. I feel like jumping through hoops to say, "well, my official title is Software Engineer, but technically I'm a programmer" is just pedantic and probably more confusing for most people.
I could see an argument for differentiating between those who participate heavily in the design and evolution of an entire codebase (as opposed to those who just pull tickets and write code), but even that has kind of just evolved into the junior/mid/senior/etc terminology.