Validating Digital Twins of the Local Universe with the Thermal Sunyaev-Zel'dovich Signal

The thermal Sunyaev-Zel'dovich (tSZ) effect provides a powerful probe of the thermal pressure of ionised gas in galaxy clusters and the cosmic web; constrained simulations reconstruct the mass and velocity fields of the local Universe. We explore how these two may be mutually informative: the tSZ signal provides a benchmark for assessing the fidelity of constrained simulations, and constrained simulations contribute information on the positions, total masses and density profiles of cosmic web structures for use in tSZ studies. We focus on cluster predictions in the Bayesian Origin Reconstruction from Galaxies (BORG) paradigm, introducing CSiBORG-Manticore, a new state-of-the-art suite of digital twins -- data-constrained posterior simulations whose initial conditions are inferred via Bayesian forward modelling. We develop a framework for scoring constrained simulations on their ability to match measured Planck Compton-$y$ maps around clusters, and use it to demonstrate improvement from previous BORG reconstructions. We further validate halo masses against weak-lensing-calibrated X-ray masses from eROSITA. We also show how high-fidelity digital twins offer a practical route to extracting additional information from tSZ data through a novel calibration of the mass-observable relation, and provide a complementary framework to purely statistical analyses of Compton-$y$ maps. This paves the way for integrating the large-scale structure information inherent in constrained simulations into the study of CMB secondary anisotropies.