agent-ui: running bash-tasks pill + flyout on the agent page

Adds a 'tasks' header pill (hidden at zero, like inbox/loose-ends) that
opens a side-panel flyout listing the agent's in-flight bash tasks from
GET /api/bash-tasks. Each row shows status (running/queued), task id,
elapsed time, and a truncated single-line command preview. Polled on the
same /api/state cycle as loose-ends (tasks complete async between turns, so
the count stays live); clicking the pill opens the flyout. Snapshot-only
v1 — SSE live-push is a possible follow-up.

frontend/packages/agent/src/app.js

@@ -135,6 +135,13 @@ window.marked = marked;
           buildLooseEndsList(lastLooseEnds));
       });
     }
+    const bashPill = $('bash-tasks-pill');
+    if (bashPill) {
+      bashPill.addEventListener('click', () => {
+        Panel.open('bash-tasks', 'tasks · ' + lastBashTasks.length,
+          buildBashTasksList(lastBashTasks));
+      });
+    }
   })();
 
   // ─── state rendering ────────────────────────────────────────────────────
@@ -909,6 +916,71 @@ window.marked = marked;
     reconcileAskBinds();
   }
 
+  // Running bash tasks: `GET /api/bash-tasks` returns the in-flight
+  // (Pending/Running) TaskFiles from the in-container bash-tasks dir. Same
+  // best-effort, silent-failure contract as loose-ends — a fetch miss keeps
+  // the pill at zero rather than surfacing stale chrome.
+  let lastBashTasks = [];
+  async function refreshBashTasks() {
+    try {
+      const resp = await fetch('api/bash-tasks');
+      if (!resp.ok) {
+        renderBashTasks([]);
+        return;
+      }
+      const data = await resp.json();
+      renderBashTasks(data.tasks || []);
+    } catch (err) {
+      console.warn('bash-tasks fetch failed', err);
+      renderBashTasks([]);
+    }
+  }
+
+  function buildBashTasksList(tasks) {
+    const wrap = el('div', { class: 'agent-inbox' });
+    if (!tasks.length) {
+      wrap.append(el('p', { class: 'side-panel-empty' },
+        'no running bash tasks.'));
+      return wrap;
+    }
+    const list = el('ul');
+    const fmtAge = (s) => {
+      if (s < 60) return s + 's';
+      if (s < 3600) return Math.floor(s / 60) + 'm';
+      if (s < 86400) return Math.floor(s / 3600) + 'h';
+      return Math.floor(s / 86400) + 'd';
+    };
+    const now = Math.floor(Date.now() / 1000);
+    for (const t of tasks) {
+      const li = el('li');
+      const running = t.status === 'running';
+      // Elapsed since the task started (running) or was queued (pending).
+      const since = running ? (t.started_at || t.created_at || now) : (t.created_at || now);
+      const elapsed = Math.max(0, now - since);
+      // Single-line, truncated command preview (the cmd can be multi-line).
+      const cmdPreview = (t.cmd || '').replace(/\s+/g, ' ').trim().slice(0, 100);
+      li.append(
+        el('span', { class: 'bash-task-status bash-task-' + t.status }, running ? '▶ running' : '◷ queued'), ' ',
+        el('span', { class: 'inbox-from' }, t.id), ' ',
+        el('span', { class: 'inbox-ts' }, (running ? '' : 'queued ') + fmtAge(elapsed) + (running ? ' elapsed' : '')),
+        el('div', { class: 'inbox-body bash-task-cmd' }, cmdPreview),
+      );
+      list.append(li);
+    }
+    wrap.append(list);
+    return wrap;
+  }
+
+  function renderBashTasks(tasks) {
+    lastBashTasks = tasks;
+    const pill = $('bash-tasks-pill');
+    const count = $('bash-tasks-count');
+    if (count) count.textContent = tasks.length;
+    if (pill) pill.hidden = tasks.length === 0;
+    Panel.refresh('bash-tasks', 'tasks · ' + tasks.length,
+      buildBashTasksList(tasks));
+  }
+
   /** Walk `pendingAskBinds` against the latest `lastLooseEnds`
    *  snapshot, pair unbound slots with the first unclaimed pending
    *  operator-bound question whose text matches, and flip already-
@@ -1282,6 +1354,10 @@ window.marked = marked;
       // db, fetched via the per-agent socket). Cold-load fetches
       // it here; turn_end refreshes it via the renderer below.
       refreshLooseEnds();
+      // Running bash tasks live in the in-container bash-tasks dir (not
+      // /api/state); same poll cadence as loose-ends. They complete async
+      // between turns, so polling on each state cycle keeps the count live.
+      refreshBashTasks();
       // Skip the re-render if nothing structurally changed. The most
       // common case is `online` polling itself — without this guard, the
       // operator's <input value> gets clobbered every cycle.