A Frame challenge:
An ancient derelict spaceship or space station orbiting Bernard's star six light years away would have to be immense to be detected from our solar system "in the near future".
Kepler-37b is the smallest known exoplanet with a radius of 0.296 that of Earth, or about 1,885 kilometers.
An extrasolar planetesimal known as WD 1145+017 b has a radius about 0.15 that of Earth, or about 955 kilometers.
SDSS J1228+1040 b is an extrasolar planetesimal with a radius of about 0.0101 that of Earth, or about 65 kilometers.
Those are the smallest dimensions of known objects orbiting other stars.
And possibly some of them are not as firmly established as claimed by the list.
And experts of the most advanced planned instruments which can be used for detecting exoplanets might be sable to say whether any planned instruments could detect objects as small as, for example, 10 kilometers in diameter, and when those instruments are planned to come on line.
I suspect that extreme lucky circumstances enabled the detection of the smallest know objects in other star systems. And an extremely advanced instrument which goes online 20 years in the future might be used for a decade or two before it makes a very lucky discovery of an object only about ten kilometers in diameter.
And I have to wonder how the artificial nature of tiny objects detected in other solar systems will be discovered.
If images of an extrasolar object are taken, and also its spectrum, and the spectrum in radially different in certain ways from that of the star, it might be deduced that the object is made of polished metal, or of some synthetic compound of great strength.
Less than thirty planets of other stars have been detected or suspected by direct imaging of those planets. The smallest of those which have estimated sizes, Candidate 1 orbiting Alpha Centauri A, has a radius of about 0.459 that of Jupiter or about 30,685 kilometers, or 4.8 times the radius of Earth.
So instruments will have to vastly improve before an object the size of an imperial star destroyer in Star Wars can be detected. And improve even more before before such an object can be determined to be artificial.
So I have my doubts about the artifact being detected, and a mission sent to Barnard's Star, in the near future.
Possibly the main character can be the world's most famous scientist, or the world's most famous astronaut, who dies suddenly and their corpse is frozen. They are brought back to life by advanced science centuries in the future, at about the time that the artifact is discovered and the expedition is planned. And because future people are much less bold and adventurous than 21st century people, and because the main character is a famous person from the past, they are selected to go on the expedition.
Maybe only recently revived people frozen centuries earlier will volunteer to go on the expedition.