> I’m not convinced that all semantics of “and” can be derived from set operations.
Totally agree. I think part of the issue is that "natural-language and" behaves differently when you apply it to different parts of speech, and everyone in this thread is thinking of a different part!
That being said, in the example sentences you gave ("I punched Bob and apologized" vs. "I apologized and punched Bob"), it's actually ambiguous whether they have equivalent meaning or not, when we ONLY consider grammar. Using ONLY the words in the sentence, the relationship between "apologized" and "punched" rests on our interpretation of "and"'s grammatical role. Taken in its usual sense as a conjunction, the two verbs are only related in the sense that the same subject performed them.
But I think you're arguing that "and" places the two verbs in sequence (which prevents the sentence from being flipped without changing meaning.) The more I think about this, the more I don't think it follows. To read the verb phrase this way, the reader has to infer a missing conjunctive adverb: ("punched Bob and [then] apologized")... and in order to make that inference, you need context from the sentence.
To make matters more complicated, we _could_ interpret the sentence in a way that doesn't imply the verbs are related: suppose the speaker is apologizing to some third party, and punches Bob for some unrelated reason. If we interpret it this way, the two sentences can be switched without changing the meaning too much.
But all this just goes to show: your core point is correct: natural languages aren't formal languages, and trying to treat them as such is an exercise in frustration.