Add pre-update/clean backup feature

- Backup deletion paths before update to sd:/backup/OmniNX/{version}
- Backup deletion paths before clean install to sd:/backup/OmniNX/pre-omninx
- Best-effort backup: continue install even if some copies fail
- Fix directory creation: ensure parent dirs exist before folder_copy
- Step 1 for update: Backup; Step 1-2 for clean: user data + pre-omninx backup

Co-authored-by: Cursor <cursoragent@cursor.com>

source/install_update.c

@@ -4,6 +4,7 @@
  */
 
 #include "install.h"
+#include "backup.h"
 #include "deletion_lists_update.h"
 #include "fs.h"
 #include "version.h"
@@ -34,6 +35,25 @@
 #define path_exists install_path_exists
 #define count_directory_items install_count_directory_items
 
+// Backup paths before update (sd:/backup/OmniNX/{version})
+int backup_before_update(const char *version) {
+    char backup_base[270];
+    s_printf(backup_base, "%s/%s", BACKUP_BASE_PATH, version);
+    return backup_deletion_lists(backup_base,
+        atmosphere_dirs_to_delete,
+        atmosphere_contents_dirs_to_delete,
+        atmosphere_files_to_delete,
+        bootloader_dirs_to_delete,
+        bootloader_files_to_delete,
+        config_dirs_to_delete,
+        switch_dirs_to_delete,
+        switch_files_to_delete,
+        root_files_to_delete,
+        misc_dirs_to_delete,
+        misc_files_to_delete,
+        NULL);
+}
+
 // Update mode: Cleanup specific directories/files
 int update_mode_cleanup(omninx_variant_t variant) {
     (void)variant;