I think my software engineering undergrad course summarized it up, and they emphasized the difference between soft eng and programming with that you can really can call any form of programming as really just playing with or handling code whereas engineering involves licensing, researching techniques that involve optimized solutions and moreover adherence to some form of moral engineering ethics that might not be written as part of law.

Moreover, I don't think theres a big issue with using programmer or engineer, but I dont think that the word programmer is stigmatized but rather because its now an older term and not as recent as software engineer which is more trendier. You could think of it as how the word "phat" was used in hip hop to really just mean cool whereas nowadays kids would be confused to hear you use the word.

I think it speaks more of a change in the era where new words are considered cooler and just spread on their own, something that probably happens all the time, just like how young people adopt new slang.

In fact, if we switched the position of programmer and engineer in terms of how they were used in history where all programmers would be used to called engineers, maybe you would instead say that the word engineers is stigmatized.