I'm not sure we can rule out a meaningful and objective measure of purposfulness, or something closely related to it.

If I saw a Martian laying five rocks on the ground in a straight line, I would label it an optimization process. Omega might tell me that the Martian is a reasonable powerful geral optimization process, currently optimizing for a target like 'Indicate direction to solstice sunrise." or "Communicate concept of five-ness to Terran". In a case like that the pattern of five rocks in a line is highly intentional.

Omega might instead tell me that the Martian is not a strong general optimization process, but that member of its species frequently arrange five stones in a line as part of their reproductive process, that would be relatively low in intentionality.

But intentionality can also go with high intelligence. Omega could tell me that the Martian is a strong general optimization agent, is currently curing Martian cancer, and smart martians just rocks in a line when they're thinking hard. (Though you might reparse that as there is a part of the martian brain that is a specialized optimizer for putting stones in a line. I think knowing whether this is valid would depend on the specifics of the thinking hard->stones in a line chain of causality.)

And if I just found five stones in a line on Mars, I would guess zero intentionality, because that doesn't constitute enough evidence for an optimization process, and I have no other evidence for Martians.