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.h

@@ -39,11 +39,7 @@ void install_preserve_update_cleanup_end(void);
 void install_set_color(u32 color);
 void install_check_and_clear_screen_if_needed(void);
 bool install_path_exists(const char *path);
-int install_count_directory_items(const char *path);
-void install_combine_path(char *result, size_t size, const char *base, const char *add);
-int install_copy_staging_root_files(const char *staging, const char *dst_root);
-int delete_path_list(const char* paths[], const char* description);
+int install_move_staging_root_files(const char *staging, const char *dst_root);
+int install_move_tree(const char *src, const char *dst_parent, const char *display_name);
+int install_delete_tree(const char *path);
 int delete_path_lists_grouped(const char *folder_display_name, ...);
-int folder_delete_single_with_progress(const char *path, const char *display_name);
-int folder_delete_progress_recursive(const char *path, int *deleted, int total, u32 start_x, u32 start_y, const char *display_name, int *last_percent);
-int folder_copy_with_progress_v2(const char *src, const char *dst, const char *display_name);