Supplementary material to DESI's publication "Clustering of DESI galaxies split by thermal Sunyaev-Zeldovich effect" to comply with the data management plan. Paper abstract The thermal Sunyaev-Zeldovich (tSZ) effect is associated with galaxy clusters — extremely large and dense structures tracing the dark matter with a higher bias than isolated galaxies. We propose to use the tSZ data to separate galaxies from redshift surveys into distinct subpopulations corresponding to different densities and biases independently of the redshift survey systematics. Leveraging the information from different environments, as in density-split and density-marked clustering, is known to tighten the constraints on cosmological parameters, like $\Omega_m$, $\sigma_8$ and neutrino mass. We use data from the Dark Energy Spectroscopic Instrument (DESI) and the Atacama Cosmology Telescope (ACT) in their region of overlap to demonstrate informative tSZ splitting of Luminous Red Galaxies (LRGs). We discover a significant increase in the large-scale clustering of DESI LRGs corresponding to detections starting from 1-2 sigma in the ACT DR6 + Planck tSZ Compton-$y$ map, below the cluster candidate threshold (4 sigma). We also find that such galaxies have higher line-of-sight coordinate (and velocity) dispersions and a higher number of close neighbors than both the full sample and near-zero tSZ regions. We produce simple simulations of tSZ maps that are intrinsically consistent with galaxy catalogs without systematic effects, and find a similar pattern of large-scale clustering enhancement with tSZ effect significance. Moreover, we observe that this relative bias pattern remains largely unchanged with variations in the galaxy-halo connection model in our simulations. This is promising for future cosmological inference from tSZ-split clustering with semi-analytical models. Thus, we demonstrate that valuable cosmological information is present in the lower signal-to-noise regions of the thermal Sunyaev-Zeldovich map, extending far beyond the individual cluster candidates. Contents data-basic-plots.zip — small archive with basic data from plots; data-extra.zip — relatively big archive with additional data; source-code.zip — Python scripts and Jupyter notebooks used for the paper. Please see README.md in each archive for more specific details. Changelog 1.0 — first release of the supplementary material corresponding to arXiv v1. 1.0.1 — added/fixed links to the paper in READMEs, data and code have not changed. 2.0 — update of the supplementary material corresponding to arXiv v2, which should be published in the Open Journal of Astrophysics.