The word didn't exist in Webster's time, so it's unclear which dictionary you're referring to, but in any case the definition is so incomplete as to be wrong.
Etymonline says, "pertaining to or characteristic of a (high) class," from 1891. https://www.etymonline.com/word/classy GCIDE says, "having elegance or taste or refinement in manners or dress," and "exhibiting refinement and high character. Opposite of low-class." WordNet says, "Elegant and fashionable." What brings all these definitions together is that something is good in the particular way that the upper class values.
It's true that many people who admire the manners of the upper class consider their behavior standards to be "high standards", and they certainly are demanding standards. But "classy" is not used to describe conformance to any demanding standards of personal behavior, such as a soldier's enthusiastic yelling and physical fitness, Clarence Darrow's unyielding advocacy of the welfare of the world's poorest, Feynman's profound mathematical learning and epistemic humility, or the brutal, unvarnished honesty demanded by Dutch society. As you know if you are a native speaker of English, none of these are considered "classy", however demanding they may be, because they do not belong to the [English and North American] upper class, which demands very high standards of etiquette, euphemism, diplomacy, fashion, and stoicism. Those virtues are "classy"; the other virtues I described above are not only not "classy" but in many cases positively opposed to "classiness".
I think all social classes today would consider the term ratfucking obscene, and believe that using obscenities is inconsistent with a high standard of behaviour?
It's interesting to look at the older roots of the word and see links to social class there but I'm not using the term in that sense. The definition I referred to is a modern one from Mirriam Webster.
On the contrary, there are many people who consider using obscenities to be praiseworthy or even obligatory under certain circumstances. Generally they belong to social classes that you evidently have carefully avoided having any experience with.
The ideological line you're laying down here is a specifically upper-class ideology, as revealed by its content, not just the words you use. Your lack of awareness of the origin of that ideology comes from does not liberate you from that origin; on the contrary, it enslaves you to it, making you an instrument of agendas you do not understand and cannot question. Please see https://news.ycombinator.com/item?id=22551881
Etymonline says, "pertaining to or characteristic of a (high) class," from 1891. https://www.etymonline.com/word/classy GCIDE says, "having elegance or taste or refinement in manners or dress," and "exhibiting refinement and high character. Opposite of low-class." WordNet says, "Elegant and fashionable." What brings all these definitions together is that something is good in the particular way that the upper class values.
It's true that many people who admire the manners of the upper class consider their behavior standards to be "high standards", and they certainly are demanding standards. But "classy" is not used to describe conformance to any demanding standards of personal behavior, such as a soldier's enthusiastic yelling and physical fitness, Clarence Darrow's unyielding advocacy of the welfare of the world's poorest, Feynman's profound mathematical learning and epistemic humility, or the brutal, unvarnished honesty demanded by Dutch society. As you know if you are a native speaker of English, none of these are considered "classy", however demanding they may be, because they do not belong to the [English and North American] upper class, which demands very high standards of etiquette, euphemism, diplomacy, fashion, and stoicism. Those virtues are "classy"; the other virtues I described above are not only not "classy" but in many cases positively opposed to "classiness".