About the size and mass of Earth
Exoplanet discovery hasn't quite dropped below the "about earth sized" detection limit yet, and we've already detected one, possibly two or three, exoplanets in orbit around the Alpha Centauri system.
Proxima Centauri b (aka or Alpha Centauri Cb) is approximately 1.27 Earth masses with a radius between 0.8 and 1.5 Earth's. Although the data only gives a minimum value on the mass.
There are also two other possible detections (that unlike Alpha Centauri Bb haven't been ruled a data anomaly yet), one of which has a radius of about 0.92 Earth's. I can't find a whole lot of information about these.
Detecting anything smaller or less massive than that is beyond current technology and even current technology is based on very precise measurements that are prone to error (as evidenced by Alpha Centauri Bb). It's the equivalent of measuring the light intensity of a lighthouse beacon vs. the same beacon with a single poppy seed placed in front of it. Which is why there are such precise measurements on the radius of exoplanets but not their mass.
Now, if your alien civilization was building something like a Dyson Swarm we here on Earth would probably start picking that up as soon as the light level of the star dipped significantly. Most exoplanet research is done with observations over the period of weeks or months, so without one of those aimed at the Alpha Centauri system, you'd have to wait on the less focused observations to pick up the dimminig. But a dyson swarm could do that pretty easily with little mass involved, simply by congregating on one side of the star. But at the same time, such a swarm could easily avoid being detected simply by making sure it is sufficiently diffuse.
How quickly that would get noticed? No idea. Assuming that at 100% light absorption that any Joe on the street with his naked eye notices that the star is missing in a few seconds and that at 0% light absorption, even the exoplanet research teams see nothing wrong after 6 months of study, then there exists some value X between these two extremes such that someone, somewhere, eventually notices and the scientific community starts aiming more powerful telescopes at the system to see what's up (and even then they might only be able to conclude that "something is happening" because the actual image of the system is still only pixels in size, but 1% dimmer than a year ago!).