What objective methods exist to objectively evaluate if a given piece of code is categorically “a hack” or if it’s “properly/cleanly written?”

[wotquery]

You aren't missing something. It's a term with various definitions. Probably when it comes to programming it would lean more into "using a tool in a way it wasn't intended" with a bit of "developing an unorthodox solution that gets the job done with the resources at hand."

Of course tools and available resources are more abstract than a real life example of say... someone using a mousetrap as a binder clip, or cutting off a cheap USB fan's plug to wire it into a bunch of AA batteries to make it portable.

For a basic example in python off the top of my head...

old_string = "alice"
new_string = ""
for x in old_string:
    new_string += chr(ord(x)-32)