Interstellar archaeology and surface engineering
My strategy emphasizes that, whatever the alien structure may be, we would be looking at its surface. Artificial surfaces tend to be highly engineered for useful thermal and optical properties. The spectra of artificial satellites, painted surfaces, skyscraper windows, and so on exhibit many features which are extremely improbable in nature. For example, skyscraper windows and spacecraft surfaces often have gold at concentrations millions of times higher than stellar dust clouds, because of gold's very good thermal and optical functions. There are also many artificial molecules used in paints, again with unique spectra that would stand out from natural galactic features. Advanced ETI may have moved on to more advanced surfaces, but whatever they use, it is very likely to have highly unnatural spectra in order to optimize its function.
My surface-engineering-based search strategy has the added benefit that it doesn't matter how large any individual structure is, so long as a collection of artifacts collectively present surfaces that look artificial enough to stand out from natural galactic spectra. It also doesn't matter whether or not ETI are operating any of a number of hypothesized high-energy nuclear technologies: natural sunlight reflected off artificial surfaces is sufficient. Thus "Fermi bubbles", hypothetical regions of other galaxies to which an ETI civilization has spread, may be most readily recognized not by features recognizable to the human eye (in any nearby large galaxy, astronomers would already have discovered them), nor by determining what kinds of structures the ETI have constructed, but analyzing, often by exhaustive computer search, spectra of different regions in galaxies for the tell-tale signatures of engineered surfaces.