I initially had some difficulty finding the file hierarchies that I was used to accessing on Windows once I migrated to Linux. These notes may be helpful in some situations.
Native Package Managers
This document is running under the assumption that you are installing Blender via the native package managers like pacman, apt, dnf, etc.
AppData equivalent is in ~/.config/blender/[version]/...
Main file hierarchy is likely located in /usr/share/blender/[version]/...
Main repo OCIO/COlormanagement files are in /usr/share/blender/[version]/datafiles/colormanagement
AUR Blender LTS OCIO files are in /opt/blender-lts/4.5/datafiles/colormanagement
Flatpak
Addons found in ~/.var/app/org.blender.Blender/config/blender/5.1/scripts/addons/
Main File directory to find studio light hdris and color management ocio files is /var/lib/flatpak/app/org.blender.Blender/current/active/files/blender/5.1/datafiles
AUR, Snapd, Etc
For additional Blender LTS installations alongside normal package managers, such as AUR in CachyOS and Arch via Paru or Yay are likely in other locations.
Blender-LTS from AUR via paru and yay usually shows up in /opt/blender-lts/[version]/... Additional files can also be found in the .config folder as listed above as well.
Blender Snap package executable is generally located at /snap/bin/blender, while the core installation files reside under /snap/blender/current/. User configuration and scripts for the snap version are usually stored in ~/snap/blender/current/.config/blender/