Interestingly, Tabby’s star is almost 1500 light years from Earth, according to Wikipedia.
So the light we’re currently seeing left the star 1500 years ago and any “alien construction” that may or may not have happened would now be 1500 years old.
If there were a culture able to build a structure around a star 1500 years ago, imagine how advanced they’d be by now.
If this really is a Dyson Sphere (or something similar), then they already were extremely advanced when they got started. Probably thousands of years ahead of our current technology.
I personally do not believe this is aliens. It’s just too improbable. Much more likely some as yet unexplained confluence of natural events, gas clouds, exploded planet, whatever.
However, the subject is interesting and if I was the boss of the James Webb, it would be a primary target under my direction.
The details of this star’s dimming was discovered by analyzing Kepler data.
One technology I do believe in: space telescopes.
The more, the merrier. The bigger, the better.
...or they could have died out yesterday on the eve of their first exploratory mission to Sol's third planet.