The birth of the intracluster medium: the evolution of multiphase gas and Lyman-$α$ haloes in a simulated $z\sim3$ protocluster

Galactic haloes host a complex, multiphase circumgalactic medium (CGM), and at high redshift are fed by cold, filamentary inflows. In contrast, mature galaxy clusters are dominated by a hot, enriched, X-ray emitting intracluster medium (ICM), with cold gas largely confined to member galaxies. However, the transition between these regimes remains poorly constrained. We present a cosmological zoom-in simulation of a massive cluster progenitor evolved to $z=2.7$, with enhanced CGM resolution to better trace the accretion, mergers and feedback events that precede the birth of the ICM. We connect this evolution to mock MgII, CII, OVI and OVII absorption, tracing low and high ionisation gas phases. We also study Lyman-$\alpha$ (Ly$\alpha$) and Balmer-$\alpha$ (H$\alpha$) haloes in emission, using radiative transfer in post-processing. Between $z\sim4.4$ and $2.7$, a major merger and AGN feedback drive an inside-out transformation, redistributing gas to larger radii and flattening density, temperature and metallicity profiles. Intermediate column MgII absorbers are rapidly destroyed, leaving a clumpier cold gas distribution associated with satellites, while gas is ionised beyond OVII as the inner halo enters the X-ray regime. An extended Ly$\alpha$ halo remains detectable even without AGN photoionisation, and evolves from filamentary to more spherical as inflowing gas is disrupted. Our fiducial model underpredicts observed central Ly$\alpha$ emission — we likely require more efficient Ly$\alpha$ production in the nuclear region, either through more effective escape of stellar Ly$\alpha$ photons or through enhanced conversion of AGN-powered ionisation into Ly$\alpha$ emission. H$\alpha$ haloes are dimmer and smaller than Ly$\alpha$, but with JWST may provide a complementary probe of the evolving CGM at this critical epoch.