Fix session list disappearing on page refresh

Frontend now fetches existing sessions from /api/sessions when SSE connects.
Previously only listened for session_start events, causing sessions to
disappear after page reload.

public/index.html

@@ -1002,6 +1002,43 @@
       }
     }
 
+    async function fetchExistingSessions() {
+      try {
+        const res = await fetch('/api/sessions');
+        if (!res.ok) {
+          console.error('Failed to fetch existing sessions:', await res.text());
+          return;
+        }
+        const sessions = await res.json();
+        sessions.forEach(session => {
+          state.sessions.set(session.id, {
+            id: session.id,
+            cwd: session.cwd,
+            command: session.command,
+            output: '',
+            outputRenderedLength: 0,
+            expanded: false,
+            state: 'ready',
+            prompts: 0,
+            completions: 0,
+            tools: 0,
+            compressions: 0,
+            thinking_seconds: 0,
+            work_seconds: 0,
+            mode: 'normal',
+            model: null,
+            idle_since: null,
+            git_branch: null,
+            git_files_json: null,
+            autoScroll: true,
+          });
+        });
+        renderSessions();
+      } catch (error) {
+        console.error('Error fetching existing sessions:', error);
+      }
+    }
+
     function connectSSE() {
       if (state.eventSource) {
         state.eventSource.close();
@@ -1016,6 +1053,7 @@
           clearTimeout(state.reconnectTimeout);
           state.reconnectTimeout = null;
         }
+        fetchExistingSessions();
       });
 
       es.addEventListener('error', () => {