What's your position on intentionality[0]? I don't put stock into anything too fancy there. Being simple about things in general, you can define a physical or mathematical system that uses optimization of some sort to drive the world toward certain states over others.
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.
It's still useful to communicate with people who don't desire to or do not tend to think in systems. You can define things any such way you'd like, of course, especially if communication is not your desire.