fix(backends,conversations,telegram,ui): a background subagent reports back as its own turn

ui/src/lib/panel/chat-view.svelte

@@ -7,7 +7,7 @@
   import { clip, fmtDateTime, fmtTime } from "$lib/format";
   import { cn } from "$lib/utils";
   import type { ActivityModel } from "./activity.svelte";
-  import { summarizeInput, toolLabel } from "./activity.svelte";
+  import { isLive, summarizeInput, toolLabel } from "./activity.svelte";
   import { cacheableHistory, historyKey } from "./history-cache";
   import { usePanelHost } from "./host";
   import Markdown from "./markdown.svelte";
@@ -48,7 +48,7 @@
 
   const tail = $derived(
     model.turns
-      .filter((turn) => turn.status === "running" || turn.startedAt > loadedAt)
+      .filter((turn) => isLive(turn) || turn.startedAt > loadedAt)
       .reverse()
   );
   const tailSize = $derived(
@@ -150,14 +150,16 @@
 
   $effect(() => {
     const timer = setInterval(() => {
-      if (model.running) {
+      if (model.live.length > 0) {
         now = Date.now();
       }
     }, TICK_MS);
     return () => clearInterval(timer);
   });
 
-  const SYSTEM_HEAD = /^\[[^\]\n]+\]/;
+  // Text the gateway or the CLI put in the user's seat: an inject header,
+  // an envelope, a subagent's report.
+  const SYSTEM_HEAD = /^(\[[^\]\n]+\]|<task-notification>)/;
   const SECONDS = /:\d{2}$/;
   const DAY_TIME = /,?\s*\d{2}:\d{2}$/;
   let openSystem = $state<Set<number>>(new Set());