Fix dashboard race condition in initial_state handler

When a new session's initial_state arrives, we now set the output
before calling renderSessions() rather than after. This prevents
renderSessionOutput() from being called before the DOM exists.

public/index.html

@@ -1169,7 +1169,7 @@
             id: data.session_id,
             cwd: '',
             command: 'claude',
-            output: '',
+            output: data.html,
             outputRenderedLength: 0,
             expanded: false,
             state: 'ready',
@@ -1186,12 +1186,14 @@
             git_files_json: null,
           };
           state.sessions.set(data.session_id, session);
+          // renderSessions() will render both the session and its output
           renderSessions();
+        } else {
+          // Session already exists, update output and re-render it
+          session.output = data.html;
+          session.outputRenderedLength = 0; // Force re-render
+          renderSessionOutput(data.session_id);
         }
-        // Replace output with current terminal state
-        session.output = data.html;
-        session.outputRenderedLength = 0; // Force re-render
-        renderSessionOutput(data.session_id);
       });
 
       es.addEventListener('output', (e) => {