It is true that the word organic has changed over time, but this represents the organic usage of words in American English. (See what I did there?) When I was in high school, I learned that the word "organic" related to the availability of carbon in living things. And probably the next significant usage trickled in with organic foods, which are grown without chemical fertilizers, pesticides, or antibiotics. And now, the word organic is often used as a modifier similar to "natural."
But this is what we ask of English. Speakers constantly transform the nature of the language into what we need it to do for us. Society changes. Ideas change. And we need for our language to reflect those changes. So some words are added or modified in usage and others are dropped and forgotten. For example, Frederick Douglass used to escape to his "growlery," a place to retreat from the world when in a bad mood. The word was invented by Dickens. A similar escape room might be a "man cave" in today's society. But while Douglass sought to escape to reflect and write, a man cave is used to escape and watch sports, lift weights, or play card games with friends. Society changed (not necessarily for the better), and the words needed changed as well.
The word "organic" is no different. Once it was necessary to distinguish the origins of life, and then the base of science grew. People needed to distinguish healthier food choices in their grocery stores. (And marketing executives needed a way to charge more for it.) In the end, all of the transformations of the word "organic" have the idea of "natural" at the core. They share similarities, and fluent speakers are capable of navigating the ways any word changes over time.