If an alien life form had tinkered with the positions of stella bodies of some kind for the purposes of harnessing energy, or for any other reason, what would evidence of that look like to an observer, i.e., us?
We wouldn't be able to tell a difference. Getting energy from gravitational assists for example will alter the rotation or orbit of an astrophysical object; however, I don't believe we could tell after the fact that the orbit/rotation was altered.
There are (theoretical) energy harnessing technologies which we may be able to see the effects of. One of the more fantastical ones is a Dyson sphere which captures all the energy/radiation given out by a star. In this case, we would see the gravity of the star affecting the surrounding area, but we wouldn't be able to see the light. We may infer that this object is not a black hole by looking at the density implied by the orbits of the planets around it. These kinds of things are still quite far away imo haha.
In Brief History of Time there is mention of towing a white dwarf using matter as a kind of dangling carrot. I know this is fanciful for us but I'm thinking if a human can imagine it, maybe a more advanced alien race could actually do it.
Well, if we see 1 big ball of mass moving in a line "towing" a white dwarf, we may suspect something. But I'm saying you wouldn't be able to tell the difference AFTER the fact. Since you don't know the initial velocity, you can't be sure that the altered orbit wasn't the original orbit in the first place.