how GAIA would estimate the tabby' star distance if a megastructure is around the star?

A dyson sphere is physically impossible to our understanding of materials science. There is no way to build a structure that gigantic that wouldn't collapse on itself in the star's gravity. A much more possible idea is a dyson swarm

Actually Dyson sphere means the same thing as Dyson swarm. Sometimes people use the term incorrectly, but a Dyson sphere definitely isn't a single solid structure.

https://en.wikipedia.org/wiki/Dyson_sphere

The concept of the Dyson sphere was the result of a thought experiment by physicist and mathematician Freeman Dyson, when he theorized that all technological civilizations constantly increased their demand for energy. He reasoned that if human civilization expanded energy demands long enough, there would come a time when it demanded the total energy output of the Sun. He proposed a system of orbiting structures (which he referred to initially as a shell) designed to intercept and collect all energy produced by the Sun.

Dyson replied, "A solid shell or ring surrounding a star is mechanically impossible. The form of 'biosphere' which I envisaged consists of a loose collection or swarm of objects traveling on independent orbits around the star."

The variant closest to Dyson's original conception is the "Dyson swarm". It consists of a large number of independent constructs (usually solar power satellites and space habitats) orbiting in a dense formation around the star.

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