Here is Karl Barth's commentary:
What does "knowledge of good and evil" mean? The expression is obviously too concrete to allow us to accept the interpretation of Wellhausen (Prolegomena, p. 300 f., etc.) that its reference is to science and our general knowledge of things. Indeed, if this were so, it would be impossible to see why God should prohibit this to man and thus prohibit progress from childish ignorance to culture, or why the saga should regard this progress as deadly. For this reason other writers (e.g., Delitzsch) have thought in terms of the problem of progress from childish innocence to moral decision. Knowledge of good and evil characterises intellectual maturity and moral decision.Church Dogmatics 3.1, The Doctrine of Creation, p. 285
I found Julius Wellhausen's perspective intriguing (and ultimately misplaced), particularly because he is best known as the first main proponent of the Documentary Hypothesis.
To me equating this "knowledge" with modern academic knowledge is just reading into the text modern (particular German modernist academic) preconceptions and concerns. Wellhausen's view reflects poorly on his scholarship.
So what does Barth himself think?
He first emphasises how ones view should be shaped by other Old Testament passages about "good and evil". After a survey he concludes
The question frequently raised whether we are to understand by "good and evil" what is morally right and wrong, or useful and useless, or pleasant and unpleasant, cannot be answered as though these were alternatives. The Old Testament concepts of tobh and ra' embrace all these things in the instances adduced. To know good and evil is to know right and wrong, salvation and perdition, life and death; and to know them is to have power over them and therefore over all things. The Genesis saga in its account of the fall, and in agreement with the rest of the Old Testament, undoubtedly tells us that man has seized this knowledge and power to his own undoing, and that he must now live in the possession of this knowledge and power.
Church Dogmatics 3.1, The Doctrine of Creation, p. 287