agent page: dashboard back-link + last-turn timing chip

title bar grows a '↑ DASHB04RD' link next to the rebuild button —
opens the host dashboard in a new tab so the operator can pivot
between agents without losing the live tail. uses the dashboardPort
already plumbed via /api/state.

state row picks up a 'last turn 12.3s' chip that fills in when
state transitions away from thinking. format: ms / s.s / m s.
hidden until the first turn completes.

hive-ag3nt/assets/app.js

@@ -65,16 +65,25 @@
       `░▒▓█▓▒░  ${label}  ░▒▓█▓▒░  hyperhive ag3nt  ░▒▓█▓▒░`;
     const title = $('title');
     title.textContent = `◆ ${label} ◆ `;
+    // ↑ DASHB04RD — back-link to the host dashboard. Opens in a new
+    // tab to keep the agent page anchored where the operator is.
+    const dashUrl = `${location.protocol}//${location.hostname}:${dashboardPort}/`;
+    title.append(
+      el('a', {
+        href: dashUrl, target: '_blank', rel: 'noopener',
+        class: 'btn-dashlink', title: 'host dashboard',
+      }, '↑ DASHB04RD'),
+      ' ',
+    );
     const btn = el('a', {
       href: '#', class: 'btn-rebuild', id: 'rebuild-btn',
     }, '↻ R3BU1LD');
     btn.addEventListener('click', (e) => {
       e.preventDefault();
       if (!confirm(`rebuild ${label}? container will hot-reload.`)) return;
-      const url = `${location.protocol}//${location.hostname}:${dashboardPort}/rebuild/${label}`;
       const f = document.createElement('form');
       f.method = 'POST';
-      f.action = url;
+      f.action = `${dashUrl}rebuild/${label}`;
       document.body.appendChild(f);
       f.submit();
     });
@@ -310,6 +319,13 @@
   }
   function setState(next) {
     if (next === stateName) return;
+    // Capture the just-ending state's duration when leaving 'thinking'
+    // so the operator can eyeball turn length without scrolling the
+    // terminal back.
+    if (stateName === 'thinking' && next !== 'thinking') {
+      const elapsedMs = Date.now() - stateSince;
+      renderLastTurn(elapsedMs);
+    }
     stateName = next;
     stateSince = Date.now();
     const badge = $('state-badge');
@@ -321,6 +337,16 @@
     }
     renderStateBadge();
   }
+  function renderLastTurn(ms) {
+    const el_ = $('last-turn');
+    if (!el_) return;
+    let s = '';
+    if (ms < 1000) s = ms + 'ms';
+    else if (ms < 60_000) s = (ms / 1000).toFixed(1) + 's';
+    else s = Math.floor(ms / 60_000) + 'm ' + Math.floor((ms / 1000) % 60) + 's';
+    el_.textContent = '· last turn ' + s;
+    el_.hidden = false;
+  }
   function startStateTicker() {
     if (stateTickTimer) return;
     stateTickTimer = setInterval(renderStateBadge, 1000);