Distributions of the observed count rate C_R (top panel) and the BCG stellar mass M_⋆, BCG (left panel) as functions of the cluster redshift for the eRASS1 clusters studied in this work. The clusters are colour-coded as in Fig. 1. We note that a clear dependence of the BCG stellar mass on the cluster redshift is revealed in the bottom panel, which arises from the X-ray selection primarily favoring massive clusters at high redshift.