fix(playout): HLS preview path + live elapsed counter

- nginx.conf: add /media/live/ location serving from the media volume
  mount. CasparCG sidecar writes HLS preview to /media/live/<id>/ but
  nginx only had /live/ (capture volume). Without this, preview
  requests returned the SPA shell instead of the .m3u8 playlist.
- ProgramMonitor: add live elapsed counter (MM:SS, ticks every 500ms)
  driven by engine.currentItemStartedAt. Shows alongside clip index.
  Adds a ⚠ pip when lastError is set (e.g. NDI SDK missing) without
  blocking operation.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

services/web-ui/nginx.conf

@@ -61,7 +61,7 @@ server {
         add_header Cache-Control "no-cache, no-store, must-revalidate";
     }
 
-    # Live HLS — served from /live (bind-mounted shared volume), low cache so playlist refreshes
+    # Live HLS — served from /live (bind-mounted capture live volume)
     location /live/ {
         alias /live/;
         types { application/vnd.apple.mpegurl m3u8; video/mp2t ts; }
@@ -69,6 +69,15 @@ server {
         add_header Access-Control-Allow-Origin *;
     }
 
+    # Playout HLS preview — CasparCG sidecar writes to the media volume under
+    # /media/live/<channel_id>/. This is a separate volume from /live/ (capture).
+    location /media/live/ {
+        alias /media/live/;
+        types { application/vnd.apple.mpegurl m3u8; video/mp2t ts; }
+        add_header Cache-Control "no-cache";
+        add_header Access-Control-Allow-Origin *;
+    }
+
     # API proxy - forward to mam-api service
     location /api/ {
         set $api_upstream http://mam-api:3000;

services/web-ui/public/screens-playout.jsx

@@ -345,12 +345,35 @@ function Transport({ channel, playlistId, items, onStatus }) {
   );
 }
 
+// ── Elapsed timer ─────────────────────────────────────────────────────────────
+function useElapsed(startedAt) {
+  const [elapsed, setElapsed] = React.useState(0);
+  React.useEffect(() => {
+    if (!startedAt) { setElapsed(0); return; }
+    const base = new Date(startedAt).getTime();
+    const tick = () => setElapsed(Math.max(0, Math.floor((Date.now() - base) / 1000)));
+    tick();
+    const id = setInterval(tick, 500);
+    return () => clearInterval(id);
+  }, [startedAt]);
+  return elapsed;
+}
+
+function fmtElapsed(secs) {
+  const h = Math.floor(secs / 3600);
+  const m = Math.floor((secs % 3600) / 60);
+  const s = secs % 60;
+  return (h > 0 ? String(h).padStart(2,'0') + ':' : '') +
+    String(m).padStart(2,'0') + ':' + String(s).padStart(2,'0');
+}
+
 // ── Program monitor ──────────────────────────────────────────────────────────
 function ProgramMonitor({ channel, engine }) {
   const videoRef  = React.useRef(null);
   const hlsRef    = React.useRef(null);
   const onAir     = channel.status === 'running';
   const previewUrl = `/media/live/${channel.id}/index.m3u8`;
+  const elapsed   = useElapsed(engine && engine.currentItemStartedAt);
 
   React.useEffect(() => {
     const vid = videoRef.current;
@@ -390,13 +413,23 @@ function ProgramMonitor({ channel, engine }) {
           <div className="po-monitor-overlay muted">Channel stopped</div>
         )}
       </div>
-      {engine && (
-        <div className="po-monitor-foot mono muted">
-          {engine.currentClip && <span className="po-monitor-clip-name">{engine.currentClip}</span>}
-          <span>clip {engine.currentIndex >= 0 ? engine.currentIndex + 1 : '–'} / {engine.playlistLength || 0}</span>
-          {engine.loop && <span> · loop</span>}
-        </div>
-      )}
+      <div className="po-monitor-foot mono muted">
+        {engine && engine.currentClip
+          ? <span className="po-monitor-clip-name">{engine.currentClip}</span>
+          : <span>{onAir ? 'Idle' : 'Stopped'}</span>}
+        {engine && engine.currentIndex >= 0 && (
+          <span style={{ marginLeft: 'auto', display: 'flex', gap: 10 }}>
+            <span style={{ color: 'var(--success)', fontVariantNumeric: 'tabular-nums' }}>
+              {fmtElapsed(elapsed)}
+            </span>
+            <span>clip {engine.currentIndex + 1}/{engine.playlistLength || 0}</span>
+            {engine.loop && <span>↺</span>}
+          </span>
+        )}
+        {engine && engine.lastError && (
+          <span style={{ color: 'var(--warning)', fontSize: 10, marginLeft: 6 }} title={engine.lastError}>⚠</span>
+        )}
+      </div>
     </div>
   );
 }