Context. Red giants are increasingly used as stellar population tracers due to their well-understood evolution and the availability of asteroseismic observables. However, stellar binarity can alter observable properties and introduce strong biases. Aims. We aim to assess a holistic picture of the binary population and evolution in the red-giant phase by characterizing the sample of binaries hosting oscillating red giants from a combination of large asteroseismic, spectroscopic, and astrometric surveys. Methods. We investigated the binary properties of evolved stars in the APOKASC 3 and APO-K2 catalogs, leveraging asteroseismic constraints and Gaia DR3 non-single-star solutions. We explored the mass distribution of red-giant binary systems, analyzed the evolution of their binary fraction. We investigated the impact of stellar evolution on the orbital periods (Porb), eccentricities, radial velocity (RV) amplitudes, and the fractional radius and identifed candidate systems that may have undergone significant interactions. Results. For stars with M ≤ 1.8 M⊙, we find binary fractions ∼31% and ∼41% for oscillating and non-oscillating solar-like stars on the main sequence (MS). By using the peak frequency of the oscillation power excess (νmax) as luminosity proxy and evolutionary states, we detect a binary attrition of ∼69% and ∼81% on the low- and high-luminosity red-giant branch (RGB) and an additional ∼38% to the red clump (RC), with respect to the MS. Binaries hosting RC and secondary-clump stars (2RC) are largely depleted at Porb ≲ 500 and ≲200 days, respectively. We identify a population of rapidly rotating RC stars in short-period orbits as potential post-common-envelope merger products. Mass-dependent differences in binary fractions and orbital properties point to stronger binary attrition for stars with M ≤ 1.8 M⊙. Conclusions. Binarity is not the primary cause of reduced oscillation amplitudes in MS solar-like stars. The distinct mass distributions and depletion of short-period binaries in the red-giant phase underscore the impact of stellar expansion and binary interaction on stellar evolution. Helium-core burning RC systems with Porb ≲ 800─1000 days are likely shaped by past interactions, such as mass transfer or loss, which can lead to significantly biased age estimates if not accounted for. This demonstrates the importance of identifying stellar binarity when using red giants as population tracers.