Ultra-high-energy cosmic rays are particles of extraterrestrial origin with energies exceeding $10^{18}~$ eV, which are studied indirectly through the extensive air showers (EASs) they induce in the atmosphere. Determining their energy spectrum and mass composition is crucial for identifying their astrophysical sources. Sensitivity to the primary mass comes from observables related to longitudinal shower development and the muonic component. At the Pierre Auger Observatory, EASs are measured using a hybrid detection technique combining fluorescence telescopes with a Surface Detector (SD) array. The SD consists of 1,660 water-Cherenkov detectors sampling the shower footprint at ground level. To exploit the spatial and temporal information encoded in SD signals, machine learning techniques are employed to complement traditional reconstruction methods. We present an overview of these studies, including deep neural network reconstructions of the depth of the shower maximum ($X_\mathrm{max}$), a novel energy estimator with reduced composition bias, analyses targeting the muonic component of EASs, and classification applications such as photon–hadron discrimination. The adoption of these approaches has enabled new physics results, e.g. an extension of $X_\mathrm{max}$ measurements to higher energies with increased statistics. Together, they demonstrate the growing impact of machine learning on event reconstruction and physics analyses at the Pierre Auger Observatory.