I think I figured it out. I have to switch the theme I’m editing at the top of the Customizer, right?
Glad to help.
Actually, as explained on the plugin homepage (under the heading “What it’s NOT for..”), and also explained in the sticky post here at the plugin’s support forum:
“This plugin should not be used together with WordPress features such as Gutenberg Block Editor, Theme Customizer, Widgets, Menus, and other theme-related options. Doing so may result in private changes being made public on the current active theme.”
As explained in the plugin documentation, Theme Switcha is for working with theme template files while your site serves another theme to visitors. For things like customizing themes, the Customizer is all that is required.
I hope this helps, let me know if I can provide any further information.