simplified code across the app and consolidated duplicated helpers

lib/view/pages/files/widgets/file_element.dart

@@ -19,6 +19,7 @@ import '../../../../widget/details_bottom_sheet.dart';
 import '../../../../widget/downloads/download_trigger.dart';
 import '../../../../widget/prompt_dialog.dart';
 import '../../talk/widgets/highlighted_linkify.dart';
+import '../data/webdav_path.dart';
 import '../sharing/share_sheet.dart';
 import 'file_details_sheet.dart';
 import 'file_leading.dart';
@@ -26,7 +27,7 @@ import 'file_leading.dart';
 class FileElement extends StatefulWidget {
   final CacheableFile file;
   final List<String> path;
-  final void Function() refetch;
+  final VoidCallback refetch;
 
   /// When non-null, occurrences of this string in the file name are visually
   /// highlighted in the tile title. Used by the Files search delegate.
@@ -101,7 +102,7 @@ class _FileElementState extends State<FileElement>
     if (widget.file.isDirectory) {
       AppRoutes.openFolder(
         context,
-        widget.path.toList()..add(widget.file.name),
+        [...widget.path, widget.file.name],
       );
       return;
     }
@@ -116,18 +117,6 @@ class _FileElementState extends State<FileElement>
     );
   }
 
-  // All paths here are relative to the WebDAV root (matching CacheableFile.path).
-  // Root parent is the empty string ''. Folders end with '/'.
-  String _parentPathOf(String path) {
-    final stripped = path.replaceAll(RegExp(r'^/+|/+$'), '');
-    if (!stripped.contains('/')) return '';
-    final parts = stripped.split('/')..removeLast();
-    return parts.isEmpty ? '' : '${parts.join('/')}/';
-  }
-
-  String _joinPath(String folder, String name, {required bool isDirectory}) =>
-      isDirectory ? '$folder$name/' : '$folder$name';
-
   void _rename() {
     if (guardDemoAction(context)) return;
     showPromptDialog(
@@ -138,9 +127,8 @@ class _FileElementState extends State<FileElement>
       initialValue: widget.file.name,
       onConfirm: (newName) async {
         if (newName.isEmpty || newName == widget.file.name) return;
-        final parent = _parentPathOf(widget.file.path);
-        final destination = _joinPath(
-          parent,
+        final destination = webdavJoin(
+          webdavFolderPath(webdavParentSegmentsOf(widget.file.path)),
           newName,
           isDirectory: widget.file.isDirectory,
         );