I think you’ve a typo here:
'nav_menu' => array(
Replace it with:
'nav_menus' => array(
We can also check out how it’s setup in the default Twenty Seventeen theme and look further how it’s implemented within get_theme_starter_content()
:
// And nav menu items are grouped into nav menus.
case 'nav_menus' :
foreach ( $config[ $type ] as $nav_menu_location => $nav_menu ) {
// Ensure nav menus get a name.
if ( empty( $nav_menu['name'] ) ) {
$nav_menu['name'] = $nav_menu_location;
}
$content[ $type ][ $nav_menu_location ]['name'] = $nav_menu['name'];
foreach ( $nav_menu['items'] as $id => $nav_menu_item ) {
if ( is_array( $nav_menu_item ) ) {
// Item extends core content.
if ( ! empty( $core_content[ $type ][ $id ] ) ) {
$nav_menu_item = array_merge( $core_content[ $type ][ $id ], $nav_menu_item );
}
$content[ $type ][ $nav_menu_location ]['items'][] = $nav_menu_item;
} elseif ( is_string( $nav_menu_item ) && ! empty( $core_content[ $type ] ) && ! empty( $core_content[ $type ][ $nav_menu_item ] ) ) {
$content[ $type ][ $nav_menu_location ]['items'][] = $core_content[ $type ][ $nav_menu_item ];
}
}
}
break;