feat: WebSocket real-time + rAF render gate + guest board + screen picker

Classroom performance:
- WebSocket server (ws-server.js) for low-latency cursor & stroke preview
  Replaces HTTP POST per event → eliminates per-message auth overhead
  Session member cache (30s TTL) avoids SQLite query per WS message
  Fallback to HTTP POST when WS not connected
- Cursor throttle reduced 100ms → 33ms (~30fps)
- Stroke preview throttle reduced 50ms → 20ms
- whiteboard.js: render() is now rAF-gated (_doRender/_rafPending)
  Multiple render() calls within one frame collapse into one repaint
  document.hidden check — zero CPU when tab is in background
  visibilitychange listener restores canvas on tab focus

Guest board:
- guestClassroom.js route: public token-based read-only access
- guest-board.html: name entry + read-only whiteboard + SSE
- SSE: addGuestClient/removeGuestClient/emitToGuests

Screen share picker:
- Discord-style modal with tab switching (screen/window/tab)
- Live video preview before confirming share
- useExistingScreenStream() in ClassroomRTC

Fullscreen exit overlay:
- #cr-fs-exit-overlay button inside cr-board-wrap
- Visible only via CSS :fullscreen selector (touchpad users)

File sharing from library:
- Teacher picks file from library, sends as styled card in chat
- crDownloadLibraryFile() fetches with Bearer auth

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/package-lock.json

@@ -15,7 +15,8 @@
         "express": "^4.18.3",
         "jsonwebtoken": "^9.0.2",
         "multer": "^2.1.1",
-        "sharp": "^0.34.5"
+        "sharp": "^0.34.5",
+        "ws": "^8.20.0"
       },
       "devDependencies": {
         "nodemon": "^3.1.0"
@@ -2038,6 +2039,27 @@
       "engines": {
         "node": ">= 0.8"
       }
+    },
+    "node_modules/ws": {
+      "version": "8.20.0",
+      "resolved": "https://registry.npmjs.org/ws/-/ws-8.20.0.tgz",
+      "integrity": "sha512-sAt8BhgNbzCtgGbt2OxmpuryO63ZoDk/sqaB/znQm94T4fCEsy/yV+7CdC1kJhOU9lboAEU7R3kquuycDoibVA==",
+      "license": "MIT",
+      "engines": {
+        "node": ">=10.0.0"
+      },
+      "peerDependencies": {
+        "bufferutil": "^4.0.1",
+        "utf-8-validate": ">=5.0.2"
+      },
+      "peerDependenciesMeta": {
+        "bufferutil": {
+          "optional": true
+        },
+        "utf-8-validate": {
+          "optional": true
+        }
+      }
     }
   }
 }