I have no clue what this babble has to do with the concept of a "purpose" or a "telos" or an "end".
The point of "POSIWID" is that you can look at e.g. a government office that's never denied a request and make a first guess that its purpose is to rubber-stamp documents.
The heuristic you're referring to seems to be figuring out whether a system does what it's intended to, which seems to be an entirely different issue. Why overload an already useful word with seemingly contradictory semantics?
Granted, it seems like a very useful concept, just an abominably-named one.
Questions regarding if the system's conscious or "cares about anything" don't really matter.
Accepting that, you can say any system that drives towards states "intends" to do so.
Unless a system is not functioning well, is weak, or is adversarial opposed, in general what it does should be more or less what it "intends".
This isn't iron-hard, but as a first guess, that gets you "the purpose of a system is what it does".
[0]: e.g. I don't know if your definition of "telos" requires anything in that direction. If you've got definitions you can link them from the SEP (Stanford Encyclopedia of Philosophy) or similar. Maybe too far into the weeds to be useful from a cybernetics perspective though. More theological.