Move pack files instead of copying; one file-op core for all modes

Install: staging and sd:/ are on the same card, so pack folders are now
moved with f_rename (a missing target folder moves in one step, existing
ones are merged file by file). Copying is only a per-entry fallback.
The staging cleanup afterwards only removes empty folders.

Deletion: one f_stat per list entry, no full recursive count before
deleting; large folders are detected with a probe that stops after 51
entries. Progress lines count processed entries instead of needing an
extra pass for a total.

Six copy/delete walkers (fs.c + install.c) are replaced by fs_delete_tree,
fs_move_tree and fs_move_file sharing one path buffer and one copy buffer
per run; the 'alternative copy method' retry is gone. extras/hekate-ams-pro
is moved too. Backups keep copy semantics.

source/install_clean.c

@@ -29,7 +29,6 @@
 #define set_color install_set_color
 #define check_and_clear_screen_if_needed install_check_and_clear_screen_if_needed
 #define path_exists install_path_exists
-#define count_directory_items install_count_directory_items
 
 // Clean mode: Backup user data
 int clean_mode_backup(void) {
@@ -102,7 +101,7 @@ int clean_mode_restore(void) {
         set_color(COLOR_GREEN);
         gfx_printf("  [OK] Wiederherstellung abgeschlossen\n");
         set_color(COLOR_WHITE);
-        delete_path_list(clean_post_restore_dirs_to_delete, "switch/ (nach Restore)");
+        delete_path_lists_grouped("switch/ (nach Restore)", clean_post_restore_dirs_to_delete, NULL);
     }
     cleanup_backup();
     return res;
@@ -132,30 +131,9 @@ int cleanup_other_staging_directories(omninx_variant_t installed_variant) {
         gfx_printf("\nEntferne weiteren Installationsordner...\n");
         set_color(COLOR_WHITE);
 
-        int total = count_directory_items(staging);
-        u32 start_x, start_y;
-        gfx_con_getpos(&start_x, &start_y);
-
-        const char *folder_name = strrchr(staging, '/');
-        if (folder_name) folder_name++;
-        else folder_name = staging;
-
-        set_color(COLOR_CYAN);
-        gfx_printf("  Loesche: %s [  0%%] (0/%d)", folder_name, total);
-        set_color(COLOR_WHITE);
-
-        int deleted = 0;
-        int last_percent = -1;
-        int res = folder_delete_progress_recursive(staging, &deleted, total, start_x, start_y, folder_name, &last_percent);
-
-        gfx_con_setpos(start_x, start_y);
-        if (res == FR_OK) {
-            set_color(COLOR_GREEN);
-            gfx_printf("  Loesche: %s [100%%] (%d/%d) - Fertig!\n", folder_name, deleted, total);
-            set_color(COLOR_WHITE);
-        } else {
+        int res = install_delete_tree(staging);
+        if (res != FR_OK) {
             set_color(COLOR_ORANGE);
-            gfx_printf("  Loesche: %s - Fehlgeschlagen!\n", folder_name);
             gfx_printf("  [WARN] Ordner konnte nicht entfernt werden (err=%d)\n", res);
             set_color(COLOR_WHITE);
         }