Correlation of ICM properties with the central cooling time for the whole TNG-Cluster sample at z = 0. We show the correlation with the five other properties introduced in Sec. 2.3 and four new properties deduced from the Sunyaev-Zeldovich signal. The mass of each cluster is specified by the color of the dots. Black lines indicate the SCC/WCC thresholds (dotted line) and WCC/NCC thresholds (dashed line) taken from the literature (see Tab. 1). The red lines indicate the 1σ thresholds (column 2 and 3 in Tab. B.1), whereas the pink lines show the thresholds stated in column 4 and 5 of Tab. B.1. (See the text for a motivation of these thresholds.) The gray dots indicate clusters with a negative cuspiness. The five CC metrics considered in this paper as well as the two metrics computed from the SZ signal are well correlated with the central cooling time.