What Galaxy Clusters Have to Say About Dynamical Dark Energy and $H_0$

We show that, in flat $\mathrm{\Lambda }$CDM, low-redshift structure probes – cluster abundances, 3$\times$2-point analyses, and full-shape clustering – are mutually consistent, jointly delivering precise constraints on ${\sigma }_8$ and ${\mathrm{\Omega }}_{\mathrm{m}}$ that agree with geometrical datasets (CMB+BAO+SN). In $w_0{w}_a$CDM, adding clusters to the geometry dataset reduces the evidence for evolving dark energy while relaxing the $H_0$ tension, suggesting a $\mathrm{\Lambda }$CDM evolution of the late-time Universe and a sound horizon that differs from its standard value.