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The warm-hot plasma in cosmic web filaments is thought to comprise a largefraction of the gas in the local Universe. So far, the search for this gas hasfocused on mapping its emission, or detecting its absorption signatures againstbright, point-like sources. Future, non-dispersive, high spectral resolutionX-ray detectors will, for the first time, enable absorption studies againstextended objects. Here, we use the Hydrangea cosmological hydrodynamicalsimulations to predict the expected properties of intergalactic gas in andaround massive galaxy clusters, and investigate the prospects of detecting itin absorption against the bright cores of nearby, massive, relaxed galaxyclusters. We probe a total of $138$ projections from the simulation volumes,finding $16$ directions with a total column density $N_{O VII} > 10^{14.5}$cm$^{-2}$. The strongest absorbers are typically shifted by $\pm 1000$ km/swith respect to the rest frame of the cluster they are nearest to. Realisticmock observations with future micro-calorimeters, such as the Athena X-rayIntegral Field Unit or the proposed Line Emission Mapper (LEM) X-ray probe,show that the detection of cosmic web filaments in O VII and O VIII absorptionagainst galaxy cluster cores will be feasible. An O VII detection with a$5\sigma$ significance can be achieved in $10-250$ ks with Athena for most ofthe galaxy clusters considered. The O VIII detection becomes feasible only witha spectral resolution of around $1$ eV, comparable to that envisioned for LEM.

Prospects for detecting the circum- and intergalactic medium in X-ray absorption using the extended intracluster medium as a backlight