Where is the key _wp_page_template passed?

The HTML attribute name is what is sent to the server. There is some PHP code reading it and storing it with a specific key in the database.

The HTML name and the database key don’t have to be the same string. The PHP code can use a completely different name or split one value into multiple database values.

The template attribute handler does that: It takes the name page_template from page attributes metabox and stores it as _wp_page_template in the database. The leading underscore protects that field from showing up in the custom fields metabox.

See this part in wp_insert_post():

if ( !empty($page_template) && 'page' == $data['post_type'] ) {
    $post->page_template = $page_template;
    $page_templates = wp_get_theme()->get_page_templates();
    if ( 'default' != $page_template && ! isset( $page_templates[ $page_template ] ) ) {
        if ( $wp_error )
            return new WP_Error('invalid_page_template', __('The page template is invalid.'));
        else
            return 0;
    }
    update_post_meta($post_ID, '_wp_page_template',  $page_template);
}