feat(web): mark a session tab whose agent has exited

The tab now reads "exited (137)" beside the session name, drawn from the
`paneExit` field the server publishes. `applyPaneExitBadge()` owns the DOM
work, called from the incremental render path — the only path a live session
ever takes, since going from live to exited adds and removes no tab and so
never reaches the full rebuild.

An unknown answer draws nothing. A death tmux could not explain reads "exited"
with no number rather than "exited (0)", so an unexplained death and a clean
exit do not look alike. A signal death reads "exited (signal 9)".

The badge carries `data-i18n-skip`, like the status pills: it is generated
text, `i18n.js` walks inserted content, and a dictionary entry added later
would fight the renderer, whose in-place comparison is against English.

The tab also carries a `tab-agent-exited` class that mutes the status dot. That
dot is drawn from `status`, which stays `idle` or `busy` for an exited pane as
the issue requires, so without this a green or pulsing dot sits beside a badge
saying the agent is gone — the first thing a tester asked about. `status`
itself is untouched, so this is a rendering rule only. The CSS excludes the two
alert classes by hand, following the convention the rich-rail dot rules
document: a dot turning red or yellow because a session is blocked on a human
outranks "the agent exited".

The tab keeps its click behavior. X still closes it, and nothing here closes,
sweeps or restarts anything.

`docs/architecture-invariants.md` gains the mechanism under "Session data and
lifecycle", where every comparable one already lives: what the tri-state means,
the four shapes it is absent for, why the watcher cannot ride the stats
collector, why an absent `#{pane_dead_status}` is not 0, and the three things
that must never happen to an exited pane.

Refs Ark0N/Codeman#446.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

src/web/public/app.js

@@ -325,6 +325,55 @@ function parseSessionPrefix(name) {
   return null;
 }
 
+// ═══════════════════════════════════════════════════════════════
+// Exited-agent tab label (Ark0N/Codeman#446)
+// ═══════════════════════════════════════════════════════════════
+// The server publishes session.paneExit when the agent inside a local tmux
+// pane has exited while remain-on-exit kept the pane. The field is tri-state
+// and its third state is absence, which means Codeman does not know — that
+// renders as nothing here and must never read as alive.
+//
+// status and signal are each optional, because tmux can know the pane died
+// without reporting how (a SIGKILLed pane on tmux 3.2a reports neither). So an
+// absent status shows a bare "exited" rather than "exited (0)": a clean exit
+// and an unexplained one must not look the same.
+function paneExitLabel(paneExit) {
+  if (!paneExit || typeof paneExit !== 'object') return '';
+  if (typeof paneExit.signal === 'number' && paneExit.signal > 0) return `exited (signal ${paneExit.signal})`;
+  if (typeof paneExit.status === 'number') return `exited (${paneExit.status})`;
+  return 'exited';
+}
+
+// Add, update or remove one tab's exited-agent badge in place. Separate from
+// the render loop so it can be exercised directly: this is the only path a
+// session going live-to-exited ever takes, since that transition adds and
+// removes no tab and so never reaches the full rebuild.
+function applyPaneExitBadge(tab, paneExit) {
+  const label = paneExitLabel(paneExit);
+  const existing = tab.querySelector('.tab-exited-badge');
+  // Quiets the status dot too. That dot reports `status`, which stays `idle` or
+  // `busy` for an exited pane by design, so without this a green or pulsing dot
+  // sits next to a badge saying the agent is gone.
+  tab.classList.toggle('tab-agent-exited', !!label);
+  if (!label) {
+    existing?.remove();
+    return;
+  }
+  if (!existing) {
+    const badge = document.createElement('span');
+    badge.className = 'tab-exited-badge';
+    // Generated status text, like the status pills: it carries data-i18n-skip
+    // rather than a dictionary entry. Without it the translator would rewrite
+    // the badge and the next render pass would rewrite it back, because the
+    // comparison below is against the English string.
+    badge.setAttribute('data-i18n-skip', '');
+    badge.textContent = label;
+    tab.querySelector('.tab-name')?.insertAdjacentElement('afterend', badge);
+    return;
+  }
+  if (existing.textContent !== label) existing.textContent = label;
+}
+
 const DEFAULT_SHORTCUTS = [
   {
     id: 'show-shortcuts',
@@ -4968,6 +5017,11 @@ class CodemanApp {
           statusEl.className = `tab-status ${status}`;
         }
 
+        // The exited-agent badge (Ark0N/Codeman#446). A session going from live
+        // to exited changes no tab count, so the full rebuild below never runs
+        // for it and this is the only path that ever draws the badge.
+        applyPaneExitBadge(tab, session.paneExit);
+
         // Rich sidebar meta ("created 3d ago · working 12m" + pill). The stamps
         // themselves move on _tickSidebarRichTimes(); this is here for the parts
         // a tick cannot see — the state flipping, and with it the pill, the row
@@ -5268,10 +5322,15 @@ class CodemanApp {
         ? ` data-tab-state="${richRow.state}" data-tab-meta-sig="${richRow.state}:${richRow.since ? richRow.since.at : 0}:${richRow.createdAt}"`
         : '';
 
+      // '' whenever the server said nothing about this pane's agent, which covers
+      // a running pane and every session shape the field never applies to
+      // (direct-PTY, remote SSH, docker). See paneExitLabel().
+      const paneExitBadge = paneExitLabel(session.paneExit);
+
       const inlineSessionActions = this.shouldInlineSessionActions();
       const tabActionsHtml = `<span class="tab-actions"><span class="tab-gear" onclick="event.stopPropagation(); app.openSessionOptions(${escapeHtml(JSON.stringify(id))})" title="Session options" aria-label="Session options" tabindex="0">&#x2699;</span><span class="tab-detach" onclick="event.stopPropagation(); app.detachSession(${escapeHtml(JSON.stringify(id))})" title="Open in a new window" aria-label="Open session in a new window" tabindex="0">&#x29C9;</span><span class="tab-close" onclick="event.stopPropagation(); app.requestCloseSession(${escapeHtml(JSON.stringify(id))})" title="Close session" aria-label="Close session" tabindex="0">&times;</span><button type="button" class="tab-more" onclick="event.stopPropagation(); app.openTabRailActionMenu(event, ${escapeHtml(JSON.stringify(id))})" title="Session actions" aria-label="Session actions">&#x22EF;</button></span>`;
 
-      parts.push(`<div class="session-tab ${isActive ? 'active' : ''}${alertClass}${richClass}${loadState ? ' tab-loading' : ''}${this.hasTabDetachOverride(id) ? ' tab-show-detach' : ''}"${richData}${railOrderStyle} data-id="${id}" data-color="${color}" ${loadState ? `data-load-phase="${escapeHtml(loadState.phase)}"` : ''} onclick="app.handleSessionTabClick(event, ${escapeHtml(JSON.stringify(id))})" oncontextmenu="event.preventDefault(); app.startInlineRename(${escapeHtml(JSON.stringify(id))})" tabindex="0" role="tab" aria-selected="${isActive ? 'true' : 'false'}" aria-busy="${loadState ? 'true' : 'false'}" aria-label="${escapeHtml(name)} session" ${tabTooltip ? `title="${escapeHtml(tabTooltip)}"` : ''}>
+      parts.push(`<div class="session-tab ${isActive ? 'active' : ''}${alertClass}${richClass}${paneExitBadge ? ' tab-agent-exited' : ''}${loadState ? ' tab-loading' : ''}${this.hasTabDetachOverride(id) ? ' tab-show-detach' : ''}"${richData}${railOrderStyle} data-id="${id}" data-color="${color}" ${loadState ? `data-load-phase="${escapeHtml(loadState.phase)}"` : ''} onclick="app.handleSessionTabClick(event, ${escapeHtml(JSON.stringify(id))})" oncontextmenu="event.preventDefault(); app.startInlineRename(${escapeHtml(JSON.stringify(id))})" tabindex="0" role="tab" aria-selected="${isActive ? 'true' : 'false'}" aria-busy="${loadState ? 'true' : 'false'}" aria-label="${escapeHtml(name)} session" ${tabTooltip ? `title="${escapeHtml(tabTooltip)}"` : ''}>
           ${_tabIdx < 9 ? '<span class="tab-number">' + (_tabIdx + 1) + '</span>' : ''}
           ${loadState ? '<span class="tab-load-spinner" aria-hidden="true"></span>' : ''}
           <span class="tab-status ${status}" aria-hidden="true"></span>
@@ -5279,6 +5338,7 @@ class CodemanApp {
             <span class="tab-name-row">
               ${mode === 'shell' ? '<span class="tab-mode shell" aria-hidden="true">sh</span>' : mode === 'opencode' ? '<span class="tab-mode opencode" aria-hidden="true">oc</span>' : mode === 'codex' ? '<span class="tab-mode codex" aria-hidden="true">cx</span>' : mode === 'gemini' ? '<span class="tab-mode gemini" aria-hidden="true">gm</span>' : mode === 'antigravity' ? '<span class="tab-mode antigravity" aria-hidden="true">ag</span>' : mode === 'pi' ? '<span class="tab-mode pi" aria-hidden="true">pi</span>' : mode === 'grok' ? '<span class="tab-mode grok" aria-hidden="true">gk</span>' : mode === 'deepseek' ? '<span class="tab-mode deepseek" aria-hidden="true">ds</span>' : mode === 'omp' ? '<span class="tab-mode omp" aria-hidden="true">om</span>' : ''}
               <span class="tab-name" data-session-id="${id}" data-full-name="${escapeHtml(name)}">${tabLabel}</span>
+              ${paneExitBadge ? `<span class="tab-exited-badge" data-i18n-skip>${escapeHtml(paneExitBadge)}</span>` : ''}
               ${inlineSessionActions ? tabActionsHtml : ''}
               <span class="tab-detached-badge" aria-hidden="true">detached</span>
             </span>

src/web/public/styles.css

@@ -2433,6 +2433,46 @@ html[data-tab-orientation='vertical'] .tab-rail .session-tab .tab-name-prefix {
   display: inline-flex;
 }
 
+/* The agent inside the pane has exited (Ark0N/Codeman#446). Unlike the badge
+   above this one carries text the server computed, so it is added and removed
+   by the renderer rather than toggled by a class. */
+.session-tab .tab-exited-badge {
+  display: inline-flex;
+  align-items: center;
+  flex: 0 0 auto;
+  font-size: 0.55rem;
+  font-weight: 700;
+  letter-spacing: 0.04em;
+  text-transform: uppercase;
+  padding: 1px 4px;
+  margin-left: 4px;
+  border-radius: 3px;
+  white-space: nowrap;
+  background: rgba(248, 113, 113, 0.16);
+  color: var(--danger);
+}
+
+/* An exited agent quiets the status dot, which otherwise reports `status` and
+   so stays green (or pulses, for a session the exit caught mid-turn) beside a
+   badge saying the agent is gone. `status` itself is deliberately untouched —
+   `error` is the PTY-exit breaker's value and makes the browser offer a restart
+   — so this is a rendering rule only, and it matches `.tab-status.ended`.
+
+   ⚠ The two alert classes are excluded BY HAND rather than by cascade, the same
+   way the rich-rail dot rules below do it: a dot turning red or yellow because
+   a session is blocked on a human outranks "the agent exited", and this
+   selector is specific enough (0,5,0) to have beaten those (0,3,0) rules
+   otherwise. The spinner ring is a pseudo-element the skin blocks cannot reach,
+   so it needs hiding explicitly rather than by unsetting the animation. */
+.session-tab.tab-agent-exited:not(.tab-alert-action):not(.tab-alert-idle) .tab-status {
+  background: var(--text-muted);
+  opacity: 0.5;
+  animation: none;
+}
+.session-tab.tab-agent-exited:not(.tab-alert-action):not(.tab-alert-idle) .tab-status::after {
+  display: none;
+}
+
 /* ===== Tab action icons: active tab only =================================
    All three per-tab icons live in a .tab-actions wrapper (in flow; it adds
    no width of its own while the children keep the width:0 collapse above).