The Auger Engineering Radio Array (AERA) consists of 153 autonomous antenna stations deployed over 17 km² to measure the radio emission from extensive air showers initiated by cosmic rays with energies between 0.1 and 10 EeV in the 30 to 80 MHz frequency band. It operates in coincidence with the other detectors of the Pierre Auger Observatory particularly the Surface Detector (SD) and the Fluorescence Detector (FD). As the largest cosmic-ray radio detector worldwide before the recent Observatory upgrade AugerPrime, AERA has played a pioneering role in the development of radio technique for cosmic rays, providing complementary measurements and serving as a testbed for ideas that motivated the build-up of a new Radio Detector (RD) as part of AugerPrime. We report on measurements of the depth of the shower maximum using the radio footprint, demonstrating compatibility and competitive resolution with established FD results. An absolute calibration of AERA is achieved by monitoring the sidereal modulation of the diffuse Galactic radio emission for nearly a decade, confirming the long-term stability of a radio detector with no significant aging effects observed. This stability suggests that radio detectors could also be used to monitor potential aging effects in other detector systems. Additionally, we investigate the muon content of inclined air showers using hybrid SD-AERA events. Our results indicate that the muon content in measured data is consistent with expectations for iron nuclei as predicted by current-generation hadronic interaction models, confirming the well-known muon deficit for the first time with radio data. These findings reinforce the value of radio detection for cosmic-ray studies and provide a foundation for the next generation of analyses with the AugerPrime RD.