feat: add poll start/end endpoints, poll.leading WS handler, and poll state persistence

Adds POST /:id/voting/start and POST /:id/voting/end endpoints that
broadcast poll lifecycle events and persist poll state to the sessions
table. The poll.leading WebSocket message is now handled server-side
(rebroadcast + DB persist) with self-healing for polls started before
the persistence columns existed.

Co-authored-by: Cursor <cursoragent@cursor.com>

backend/database.js

@@ -63,6 +63,33 @@ function initializeDatabase() {
     // Column already exists, ignore error
   }
 
+  // Poll state columns on sessions
+  try {
+    db.exec(`ALTER TABLE sessions ADD COLUMN poll_active INTEGER DEFAULT 0`);
+  } catch (err) {
+    // Column already exists, ignore error
+  }
+  try {
+    db.exec(`ALTER TABLE sessions ADD COLUMN poll_started_at TEXT`);
+  } catch (err) {
+    // Column already exists, ignore error
+  }
+  try {
+    db.exec(`ALTER TABLE sessions ADD COLUMN poll_leading_game_id INTEGER`);
+  } catch (err) {
+    // Column already exists, ignore error
+  }
+  try {
+    db.exec(`ALTER TABLE sessions ADD COLUMN poll_leading_label TEXT`);
+  } catch (err) {
+    // Column already exists, ignore error
+  }
+  try {
+    db.exec(`ALTER TABLE sessions ADD COLUMN poll_leading_votes INTEGER`);
+  } catch (err) {
+    // Column already exists, ignore error
+  }
+
   // Session games table
   db.exec(`
     CREATE TABLE IF NOT EXISTS session_games (