feat(studio): full IDE-like file management (#147)

## Summary

- **API**: POST (create), DELETE (delete), PATCH (rename/move), POST duplicate endpoints with null-byte sanitization
- **FileTree**: right-click context menu with New File, New Folder, Rename, Duplicate, Delete
- **Drag-and-drop**: move files between folders with visual feedback and subtree guard
- **Inline editing**: rename/create inputs with filename validation
- **Header actions**: quick New File / New Folder buttons in the FILES header

Stacks on top of `feat/studio-code-quality`.

## Test plan

- [x] Right-click file → Rename, Delete, Duplicate all work
- [x] Right-click folder → New File, New Folder, Delete work
- [x] Drag file from one folder to another
- [x] Create file with invalid name (`../foo`, `a/b`) → rejected client-side
- [x] Delete currently-edited file → editor clears
- [x] Studio build succeeds

packages/studio/src/components/sidebar/LeftSidebar.tsx

@@ -26,6 +26,12 @@ interface LeftSidebarProps {
   fileTree?: string[];
   editingFile?: { path: string; content: string | null } | null;
   onSelectFile?: (path: string) => void;
+  onCreateFile?: (path: string) => void;
+  onCreateFolder?: (path: string) => void;
+  onDeleteFile?: (path: string) => void;
+  onRenameFile?: (oldPath: string, newPath: string) => void;
+  onDuplicateFile?: (path: string) => void;
+  onMoveFile?: (oldPath: string, newPath: string) => void;
   codeChildren?: ReactNode;
   onLint?: () => void;
   linting?: boolean;
@@ -42,6 +48,12 @@ export const LeftSidebar = memo(function LeftSidebar({
   fileTree: fileProp,
   editingFile,
   onSelectFile,
+  onCreateFile,
+  onCreateFolder,
+  onDeleteFile,
+  onRenameFile,
+  onDuplicateFile,
+  onMoveFile,
   codeChildren,
   onLint,
   linting,
@@ -122,16 +134,28 @@ export const LeftSidebar = memo(function LeftSidebar({
         />
       )}
       {tab === "assets" && (
-        <AssetsTab projectId={projectId} assets={assets} onImport={onImportFiles} />
+        <AssetsTab
+          projectId={projectId}
+          assets={assets}
+          onImport={onImportFiles}
+          onDelete={onDeleteFile}
+          onRename={onRenameFile}
+        />
       )}
       {tab === "code" && (
         <div className="flex flex-1 min-h-0">
           {(fileProp?.length ?? 0) > 0 && (
-            <div className="w-[140px] flex-shrink-0 border-r border-neutral-800 overflow-y-auto">
+            <div className="w-[160px] flex-shrink-0 border-r border-neutral-800 overflow-y-auto">
               <FileTree
                 files={fileProp ?? []}
                 activeFile={editingFile?.path ?? null}
                 onSelectFile={onSelectFile ?? (() => {})}
+                onCreateFile={onCreateFile}
+                onCreateFolder={onCreateFolder}
+                onDeleteFile={onDeleteFile}
+                onRenameFile={onRenameFile}
+                onDuplicateFile={onDuplicateFile}
+                onMoveFile={onMoveFile}
               />
             </div>
           )}