Approximately one hundred sources of very-high-energy (VHE) gamma rays are known in the Milky Way, detected with a combination of targeted observations and surveys. A survey of the entire Galactic Plane in the energy range from a few tens of GeV to a few hundred TeV has been proposed as a Key Science Project for the upcoming Cherenkov Telescope Array Observatory (CTAO). This article presents the status of the studies towards the Galactic Plane Survey (GPS). We build and make publicly available a sky model that combines data from recent observations of known gamma-ray emitters with state-of-the-art physically-driven models of synthetic populations of the three main classes of established Galactic VHE sources (pulsar wind nebulae, young and interacting supernova remnants, and compact binary systems), as well as of interstellar emission from cosmic-ray interactions in the Milky Way. We also perform an optimisation of the observation strategy (pointing pattern and scheduling) based on recent estimations of the instrument performance. We use the improved sky model and observation strategy to simulate GPS data corresponding to a total observation time of 1620 hours spread over ten years. Data are then analysed using the methods and software tools under development for real data. Under our model assumptions and for the realisation considered, we show that the GPS has the potential to increase the number of known Galactic VHE emitters by almost a factor of five. This corresponds to the detection of more than two hundred pulsar wind nebulae and a few tens of supernova remnants at average integral fluxes one order of magnitude lower than in the existing sample above 1 TeV, therefore opening the possibility to perform unprecedented population studies. The GPS also has the potential to provide new VHE detections of binary systems and pulsars, to confirm the existence of a hypothetical population of gamma-ray pulsars with an additional TeV emission component, and to detect bright sources capable of accelerating particles to PeV energies (PeVatrons). Furthermore, the GPS will constitute a pathfinder for deeper follow-up observations of these source classes. Finally, we show that we can extract from GPS data an estimate of the contribution to diffuse emission from unresolved sources, and that there are good prospects of detecting interstellar emission and statistically distinguishing different scenarios. Thus, a survey of the entire Galactic plane carried out from both hemispheres with CTAO will ensure a transformational advance in our knowledge of Galactic VHE source populations and interstellar emission.