You can't hear their internal radio communication from such distance using SETI antennas.
I'm just repeating what was in the reports, the researchers presumably understanding signal strength in relation to their ability to detect potential signals.
What sort of signal strength is being assumed? Similar to Earth output of radio, TV and whatever else? What would you expect a civilisation building a Dyson sphere to put out, a hundred times more, a million times more, hundreds of millions?
I don't know. I couldn't guess. Maybe something else entirely.
One good way to determine what radio signals we might be able to detect from an alien civilization is to look at how far from Earth we would be able to detect our own signals.
The answer turns out to be that space is too big for us to detect most of our rf emissions from even fairly close range; The inverse square law is against us, and if SETI was looking at a copy of the Earth from a distance of as little as a few dozen lightyears, TV signals would be very hard to discriminate from background noise, and almost impossible to decode.
That makes a lot of sense - radio engineers and designers of transmitters want to use the weakest signal possible, conversant with them being clear enough to terrestrial viewers and listeners - so they take active steps to reduce the transmission of their signals into space, using aerials designed to deflect the signals along the ground, and using only enough power to reach the maximum intended range for their station.
The exception to this is the big cold-war era active radar arrays (eg DEW), designed to illuminate small, fast-moving targets coming in from the edge of space on ballistic trajectories. These signals carried very little information, but were powerful (particularly in the earlier part of the Cold War), regular, and were deliberately transmitted away from the Earth's surface. Even these signals would be beyond the ability of current SETI detectors, or even of proposed facilities like the Square Kilometre Array, past a range of (at most) a few hundred lightyears.
Tabby's Star is about 1,480 lightyears from Earth. If we make the (rather dodgy) assumption that ~1,480 years ago they had similar radars in operation (bear in mind that ours were only in place for a few decades, so we would need to be very fortunate with the timing for that assumption to hold up), then they are still about five times as far away as our most optimistic detection range.
The Earth has only been making radio noise for a century - and already we are cutting it back dramatically, not just as a result of the end of the Cold War, but also as the use of fibre-optics and other cable based networks increases, and as the efficiency of the remaining broadcast equipment improves. It would be reasonable to assume that the Earth's life as a radio source, even if our civilization persists indefinitely, might be as short as a couple of centuries in total; and our time as a bright source, visible tens or hundreds of lightyears away, was likely only half a century or so.
Add to that that the really 'bright' signals are radar scan signals, so they are regular and 'bright', but carry very little information. If we detected such signals, we might well attribute them to an unknown natural source, rather than to aliens, as we have been caught out before (eg by Pulsars). A TV, voice or morse code signal couldn't be explained away so easily - but these sources are far weaker, and to detect them would require much larger arrays of radio telescopes than would be needed to pick up the DEW Radar signals.
I would expect a civilization that was building a Dyson sphere to be putting out very little radio noise; They might well use laser communications in their space program (more efficient and less prone to interception than radio), and fibre optic or other cable technology on the surface of their planet. Certainly that's the way we are heading, and we are nowhere close to being able to consider building any kind of solar orbiting megastructures.
The absence of detectable and clearly artificial radio frequency transmissions from that star system is therefore to be expected; It would be expected if they were as 'noisy' as we were at our peak radio brightness, and is even more to be expected if they are (as I think would be almost certain) far less noisy than our rather lowly civilization.
Assuming they have a SETSI (Search for Extra Tabby's Star Intelligence) program with far larger collection area than our puny Square Kilometre effort (if they are at 5x the SKA detection range, then they need to have a 25x larger array), and that they have selected Sol as a possible life-hosting star, they might see our first powerful signals in about 1,430 year's time. Reversing the polarity, we can say that if they had an identical history to ours, and if they started building their Dyson sphere a thousand years after the end of their Cold War era, then
we could detect
their radar 'leakage' in about the year 2396 - but only if we have built a SETI detection array on the order of 25 - 100 km
2, and only if we are including Tabby's star as one of our target systems to listen to.
In short, even if we got lucky and pointed our ears directly at a star which hosted a 'radio noisy' civilization, we might not hear a peep on our radio telescopes. So while an unambiguously artificial signal that was demonstrably generated outside our solar system would be positive evidence for ETI, its absence tells us nothing very much either way.
