Which action is triggered when a theme was modified?

Anytime changes are saved in the Customizer, there is a customize_save_after hook.

For theme updates, you can use the upgrader_process_complete hook – you pass it various arguments including 'type' => 'theme'.

I don’t think there are any WordPress-specific hooks for when files of a child theme are modified. This typically happens via FTP, rather than wp-admin, so it wouldn’t have any hooks. You could possibly write something yourself to check the server’s modified timestamp on all the theme files, but that might be fairly server-intensive to check frequently.