Dependence of the X-ray-inferred velocity dispersion of the ICM on cluster mass (M_200c) and central SMBH properties according to TNG-Cluster. For the latter, we show SMBH mass (M_BH, the single largest in each halo), instantaneous accretion rate (Ṁ_BH), and accumulated kinetic feedback energy (E_kin). The solid (dashed) line represents the best-fit linear relation between the spectral-fitting (mass-weighted) velocity dispersion and cluster mass or SMBH properties. Cool-core clusters in the Perseus mass range exhibit larger levels of turbulence if they host a more massive SMBH, a SMBH that is accreting at higher rates, or a SMBH that has released more kinetic feedback on its surroundings throughout its life time.