Not yet reviewed by Pith; the record is open.

The intracluster medium (ICM) of galaxy clusters encodes the impact of the physical processes that shape these massive halos, including feedback from central supermassive black holes (SMBHs). In this study, we examine the gas thermodynamics, kinematics, and the effects of SMBH feedback on the core of Perseus-like galaxy clusters with a new simulation suite: TNG-Cluster. We first make a selection of simulated clusters similar to Perseus based on the total mass and inner ICM properties, such as their cool-core nature. We identify 30 Perseus-like systems among the 352 TNG-Cluster halos at $z=0$. Many exhibit thermodynamical profiles and X-ray morphologies with disturbed features such as ripples, bubbles, and shock fronts that are qualitatively similar to X-ray observations of Perseus. To study observable gas motions, we generate XRISM mock X-ray observations and conduct a spectral analysis of the synthetic data. In agreement with existing Hitomi measurements, TNG-Cluster predicts subsonic gas turbulence in the central regions of Perseus-like clusters, with a typical line-of-sight velocity dispersion of 200 km/s. This implies that turbulent pressure contributes $< 10\%$ to the dominant thermal pressure. In TNG-Cluster, such low (inferred) values of ICM velocity dispersion coexist with high-velocity outflows and bulk motions of relatively small amounts of super-virial hot gas, moving up to thousands of km/s. However, detecting these outflows in observations may prove challenging due to their anisotropic nature and projection effects. Driven by SMBH feedback, such outflows are responsible for many morphological disturbances in the X-ray maps of cluster cores. They also increase both the inferred and intrinsic ICM velocity dispersion. This effect is somewhat stronger when velocity dispersion is measured from higher-energy lines.