By default config files, plugins and themes are stored in .obsidian.
You can have different configurations for your devices:
To have different configurations on mobile and desktop (e.g. to choose which panes are open on which, different themes, etc), choose a different folder for the configuration of one of your devices in About > Override config folder. For workspaces, you can alternatively configure your cloud service to ignore the workspace file found in .obsidian/workspace.
You should first copy over your current configuration to the new folder and then change that option.