[Little Ray]

Not sure a Dyson sphere is a good way to hide. The change to the star’s signature might be a dead giveaway. After all, it attracted our notice.
And there would be no reason to collect the energy if the civilization has access to the stars. If it is a Dyson Sphere, then it likely means that they can’t escape their system in any efficient fashion, so they are maximizing on the resources they have.

[who_would_fardels_bear]

Because of the time it takes to create, and because any advanced menacing civilization will have mapped out all of the stars in their neighborhood, I agree with you that it wouldn't work that well as a hole to hide in.

However, that's one of the reasons Dyson mentioned, and it is a major plot point of some sci-fi novels.

There are even people trying to figure out ways of detecting completed Dyson Spheres by use of principles such as black body radiation from the exterior of the sphere, etc.