refactor: prevent overwriting existing session on reconnect and improve player identity handling

public/js/main.js

@@ -19,7 +19,11 @@ function showToast(msg) {
 function handleConnected(msg) {
   state.playerId = msg.playerId;
   if (msg.sessionId) {
-    cacheSessionId(msg.sessionId);
+    // Don't clobber an existing session on reconnect; only set if none exists yet.
+    const existing = localStorage.getItem('sessionId');
+    if (!existing) {
+      cacheSessionId(msg.sessionId);
+    }
   }
   const stored = localStorage.getItem('playerName');
   if (stored) {