fix: clear stale busy state after session recovery

Reconcile session status after materializing recovered messages
Return composer from stop to send when the server reports idle

packages/ui/src/sync/sync-context.tsx

@@ -248,6 +248,7 @@ async function materializeSessionFromServer(
   store: StoreApi<DirectoryStore>,
   options?: SessionMaterializationRequest & { isStale?: () => boolean },
 ) {
+  const statusBeforeMaterialization = store.getState().session_status?.[sessionID]
   syncDebug.recovery.materializing({
     reason: options?.reason ?? "ensure-session-messages",
     directory,
@@ -282,11 +283,15 @@ async function materializeSessionFromServer(
         info: stripMessageDiffSnapshots(record.info),
         parts: record.parts ?? [],
       })),
-      { skipPartTypes: RECONNECT_SKIP_PARTS },
-    )
-    return { message: materialized.message, part: materialized.part }
-  })
-}
+      { skipPartTypes: RECONNECT_SKIP_PARTS },
+    )
+    return { message: materialized.message, part: materialized.part }
+  })
+
+  if (statusBeforeMaterialization && statusBeforeMaterialization.type !== "idle" && !options?.isStale?.()) {
+    await resyncDirectorySessionStatuses(directory, store, [sessionID], "authoritative")
+  }
+}
 
 // Module-level refs for notification viewed check.
 // Used to determine if user is currently viewing the session when a notification arrives.