HYPERION: The cold interstellar medium of rapidly growing z>6 quasars. Diverse gas reservoirs, dust enrichment, and feedback signatures

Luminous quasi-stellar objects (QSOs) at z>6 host some of the most rapidly assembled super-massive black holes (SMBHs) in the early Universe. Characterising their cold interstellar medium (ISM) is essential to determine whether extreme SMBH growth is accompanied by similarly rapid host-galaxy assembly. We investigated the molecular gas, cold dust, star formation, gas-to-dust ratio, and ionised ISM of ten HYPerluminous quasars at the Epoch of ReionizatION (HYPERION) QSOs using new ALMA Band 3 observations targeting CO(6--5) and the underlying sim100 GHz continuum, complemented by archival and literature ALMA/NOEMA data. We detect sim100 GHz continuum emission in eight targets and CO(6--5) emission in four QSO hosts -- J025--33, J083+11, J231--20, and J0252--0503 -- as well as in the companion of J231--20. The inferred molecular gas masses are of order 10^ 10 M_⊙, while the non-detections imply upper limits of a few 10^9 M_⊙, indicating a broad range of molecular reservoirs within the HYPERION population. For J025--33 and J083+11, the far-infrared (FIR) spectral energy distributions (SEDs) are well sampled and yield low dust temperatures T_ ̊m dust =36^ +13 _ -7 K and 32^ +4 _ -3 K, respectively, well below the average value for z>6 QSOs. Combining gas and dust masses, we find a gas-to-dust ratio (GDR) for J083+11, $ ̊m GDR =16^ +5 _ -4 $, among the lowest measured in a high-redshift QSO host. We also detect NII łambda 205,μm emission in J025--33 and tentatively in J083+11, suggesting dense or highly structured ionised gas. Finally, we identify a tentative connection among T_̊m dust, the X-ray photon index Γ, and the iv velocity shift. These trends may indicate that more powerful winds redistribute dust away from the central active galactic nuclei (AGNs) heating source, lowering its temperature and weakening the connection between the large-scale dust reservoir and the X-ray corona. Overall, HYPERION QSOs emerge as a heterogeneous population in which SMBH growth, star formation, gas consumption, enrichment, and feedback are not necessarily synchronised.