feat(web): add Vue workspace with file tree, tabs, autosave and live sync

- Login and first-run setup screens
- File tree with inline create/rename, context menu, drag-and-drop
  move and trash with undo; all operations update the UI first and roll
  back on failure
- Tabs keep a CodeMirror state each; edits autosave after 500 ms with
  If-Match revisions, unsent edits persist in IndexedDB, and conflicts
  or remote deletions surface as banners with explicit choices
- WebSocket events sync external edits, moves and deletions into open
  tabs; reconnects trigger a full resync
- Pasted or dropped images show instantly and upload to note.assets/
- Responsive layout with a swipe-in sidebar drawer on phones
- Switch to TypeScript 6: vue-tsc does not support TypeScript 7 yet

web/tsconfig.json

@@ -12,5 +12,5 @@
     "skipLibCheck": true,
     "noEmit": true
   },
-  "include": ["src", "vite.config.ts"]
+  "include": ["src/**/*.ts", "src/**/*.vue", "vite.config.ts"]
 }