fix(sessions): correct session state categorization

- Backend now returns stopped and error sessions too
- Active sessions include running/building/pending
- Recent sessions show stopped/error only
- Status badge shows actual status (running/building/pending)

apps/web/src/pages/sessions.tsx

@@ -92,12 +92,12 @@ export const SessionsPage = () => {
   }, [selectedProject]);
 
   const activeSessions = useMemo(
-    () => sessions.filter((s) => s.status === "running"),
+    () => sessions.filter((s) => ["running", "building", "pending"].includes(s.status)),
     [sessions]
   );
 
   const recentSessions = useMemo(
-    () => sessions.filter((s) => s.status !== "running").slice(0, 5),
+    () => sessions.filter((s) => ["stopped", "error"].includes(s.status)).slice(0, 5),
     [sessions]
   );
 
@@ -259,7 +259,7 @@ export const SessionsPage = () => {
                           </a>
                         </p>
                       )}
-                      <span className="status-badge running">running</span>
+                      <span className={`status-badge ${session.status}`}>{session.status}</span>
                     </div>
                     <div className="session-actions">
                       {session.url ? (