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/fs.h

@@ -6,15 +6,31 @@
 #pragma once
 #include <utils/types.h>
 
+#define FS_PATH_MAX 512
+
+// Called once per processed entry (file or folder) by the tree walkers.
+typedef void (*fs_progress_cb)(void *ctx);
+
 // Error code to string
 const char *fs_error_str(int err);
 
-// File/folder operations - returns 0 on success
+// File/folder operations - return FR_OK (0) on success
 int file_copy(const char *src, const char *dst);
-int folder_copy(const char *src, const char *dst);
+int folder_copy(const char *src_dir, const char *dst_parent); // copies into dst_parent/<name>
 int folder_delete(const char *path);
 
-// File logging
+// Delete a file or folder tree (missing path = FR_OK).
+int fs_delete_tree(const char *path, fs_progress_cb cb, void *ctx);
+// Move a file, replacing dst (rename, copy as fallback).
+int fs_move_file(const char *src, const char *dst);
+// Move folder src_dir into dst_parent/<name>, merging into an existing folder.
+int fs_move_tree(const char *src_dir, const char *dst_parent, fs_progress_cb cb, void *ctx);
+// Count entries below path; stops at limit (0 = count everything).
+u32 fs_count_items(const char *path, u32 limit);
+// Free the shared copy buffer.
+void fs_release_buffers(void);
+
+// File logging (enabled via debug.ini log=1)
 void log_init(const char *path);
 void log_close(void);
 void log_write(const char *fmt, ...);