In the short term they might not care, and for an old civilization the short term might be a few hundred years. If they are anything like current day humanity, we would end up interacting with a tiny portion of their population like some middle manager at an interstellar mega corp or xenology students on a grant from their nearest university.

We won’t be important, and certainly won’t be making any appreciable difference good or bad to their civilazation as whole.

Worst case scenario that I think is plausible is that they are so decentralized that one of their warlords would come over and set up an empire on top of us for a few hundred years before the central authority realizes anything.

It’s interesting that you automatically assume they are hungry for scarce or rare resources. It is possible they live in a post scarcity society, but as a member of the human society you still automatically go to the thing that causes most of the wars and conflicts on this world.

A resource does not have to be material. It can be something made up, perhaps their version of an ever watching ghost in the sky, something that gives them purpose and motivates to continue on even though they already have everything.

But yes, slightly biased. No real reference material to speak of though :P

There was one Babylon 5 episode where an alien probe approaches the station and broadcasts a bunch of scientific questions that if we answer correctly, they will grant us knowledge beyond our dreams.

The final decision was to move the probe far enough from the station, broadcast the data, and watch as it predictably self-destructed in an explosion that would have taken out the station itself and all surrounding ships.

In USENET, the showrunner said that he based this idea on a US Military recommendation that if aliens try to contact us we should ignore them, basically play dumb so we don't seem advanced enough to bother with, just in case they ARE seeking potentially dangerous civilizations to destroy before they get too far...