Wordpress - Where does Wordpress store the users customization in the theme

That information is stored in the MySQL database, not in files like you may be thinking of. They aren't stored in .php or .html files.

If you want to "see" how and where that data is stored the easiest way is to browse the database using a tool like PhpMyAdmin.

NOTE: Technically, there are files associated with the MySQL database but they aren't easy to get to and you can't read them except through the interface provided by the MySQL engine.

WordPress does not save anything in files. All settings are stored in your database, normally the options table. Posts are stored in posts and postmeta.

You can have a look at the Database Description to get a better understanding.