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_clean.c

@@ -11,6 +11,7 @@
 #include "gfx.h"
 #include "version.h"
 #include <libs/fatfs/ff.h>
+#include <utils/sprintf.h>
 #include <string.h>
 
 #undef COLOR_CYAN
@@ -31,6 +32,26 @@
 #define path_exists install_path_exists
 #define count_directory_items install_count_directory_items
 
+// Backup paths before clean install (sd:/backup/OmniNX/pre-omninx)
+int backup_before_clean(void) {
+    char backup_base[270];
+    s_printf(backup_base, "%s/%s", BACKUP_BASE_PATH, PRE_OMNINX_LABEL);
+    return backup_deletion_lists(backup_base,
+        clean_atmosphere_dirs_to_delete,
+        clean_atmosphere_contents_dirs_to_delete,
+        clean_atmosphere_files_to_delete,
+        clean_bootloader_dirs_to_delete,
+        clean_bootloader_files_to_delete,
+        clean_config_dirs_to_delete,
+        clean_switch_dirs_to_delete,
+        clean_switch_files_to_delete,
+        clean_root_files_to_delete,
+        clean_misc_dirs_to_delete,
+        clean_misc_files_to_delete,
+        old_version_files_to_delete,
+        NULL);
+}
+
 // Clean mode: Backup user data
 int clean_mode_backup(void) {
     set_color(COLOR_CYAN);