In general, how does one determine whether X in HPMOR is supposed to [represent / be commentary on] Y?

Usually it more or less outright says it in the title.

Congratulations, you have just discovered the difference between art and design. If Azkaban had been designed to be a commentary on muggle prisons, the connection would have had to have been made explicit within the text. The fact that Eliezer pointed out the connection does not mean he consciously tried to make it explicit in the text. Since the connection is implicit rather than explicit, the commentary is an artistic interpretation of the text. You don't need to feel justified in an artistic interpretation.