Context. The current observational status of the hot (log T (K) > 5.5) intergalactic medium (IGM) remains incomplete. While recent X-ray emission and Sunyaev-Zeldovich effect observations from stacking large numbers of Cosmic Web filaments have yielded statistically significant detections of this phase, direct statistically significant measurements of single objects remain scarce. The lack of such a sample currently prevents a robust analysis of the cosmic baryon content composed of the hot IGM, which would potentially help solve the cosmological missing baryons problem. Aims. In order to improve the observationally challenging search for the missing baryons, we utilise the theoretical avenue afforded by the EAGLE simulations. Our aim is to get insights into the metal enrichment of the Cosmic Web and the distribution of highly ionised metals in the IGM. Our goal is to aid in the planning of future X-ray observations of the hot intergalactic plasma. Methods. We detected the filamentary network by applying the Bisous formalism to galaxies in the EAGLE simulation. We characterised the spatial distributions of oxygen and O vii and studied their mass and volume filling fractions in the filaments. Since oxygen is formed in and expelled from galaxies, we also studied the surroundings of haloes. We used this information to construct maps of the O vii column density and determine the feasibility of detecting it via absorption with Athena X-IFU. Results. Within EAGLE, the oxygen and O vii number densities drop dramatically beyond the virial radii of haloes. In the most favourable scenario, the median extent of O vii above the Athena X-IFU detection limit is ≈ 700 kpc. Since galaxies are relatively far apart from one another, only ∼ 1% of the filament volumes are filled with O vii at high enough column densities to be detectable by X-IFU. The highly non-homogeneous distribution of the detectable O vii complicates the usage of the measurements of the intergalactic O vii absorbers for tracing the missing baryons and estimating their contribution to the cosmic baryon budget. Instead, the detectable volumes form narrow and dense envelopes around haloes, while the rest of the O vii is diluted at low densities within the full filament volumes. This localised nature, in turn, results in a low chance (∼10-20% per sight line) of detecting intergalactic O vii with Athena X-IFU within the observational SDSS catalogue of nearby filaments. Fortunately, with deeper filament samples, such as those provided via the future 4MOST 4HS survey, the chances of intercepting an absorbing system are expected to increase up to a comfortable level of ∼ 50% per sight line. Conclusions. Based on EAGLE results, targeting the Cosmic Web with Athena may only result in tip-of-the-iceberg detections of the intergalactic O vii, which is located in the galaxy outskirts. This would not be enough to conclusively solve the missing baryon problem. However, the projection of many filaments into a single line of sight will enable a useful X-ray observation strategy...