Scientists use the term "technosignatures", which you can google for more info. But broadly: radio signals, infrared from megastructures, optical signals like laser pulses. We haven't put a huge amount of effort in searching for such signatures, but there has been some.
Another possibility is we're looking for the wrong techno signatures, or just haven't conceived what the technosignatures for a 10,000-year technologically advanced civilization are.
We've been a techno-civ for what? Maybe only 200-ish years? Our paradigm is gobble up all the energy and grow at all costs. So extrapolate that out, and the logical conclusion is a dyson megasphere that radiates all over the infrared.
But then again, that paradigm is careening us towards an environmental and ecosystem collapse: the hunger for infinite growth is warming our climate, it's unclear whether our nuclear-armed social structures can handle the coming disruptions and migrations, and if we don't kill ourselves, unclear how big a population all the environmental degradation and pollution can support.
So we can project our cute 200-year-old patterns out to a maybe-discoverable 10,000-year civilization driven by the same motivations and flows, but those extrapolations quickly run up against some pretty existential pragmatic threats.
Maybe the answer is we aren't seeing any of the technosignatures because the techonsignatures on the other side of the Great Filter look very different from the ones we conceive of now.
Thing is, though, it kind of assumes megastructures. AIUI Earth is already getting less radio-noise-y, as fibre-optics take over, and would be difficult for us to detect from the next star (at least to detect the technological civilisation; the biosignatures would be obvious).
Maybe people just don't _actually_ build that many megastructures.
I’m personally not convinced advanced civilizations would necessarily exhibit such technosignatures at all. I even go as far and ask are you sure if an advanced civilization was living and mining in Saturn’s rings we would even notice? If one considers the scales of things and realizes how big the Saturn system is relative to Earth then I doubt they can be so confident we would even notice our neighbors in the solar system yet.