feat: add formatLastSeen and buildOfflineTileHTML functions

- Add formatLastSeen(ms) to format millisecond timestamps into relative
  strings (Xs ago, Xm ago, Xh ago, Xd ago, Never for null)
- Add buildOfflineTileHTML(source) to render unreachable device tiles
  with Offline badge and last-seen timestamp
- Both functions added after buildAuthTileHTML in app.js
- Both exported via module.exports
- 7 new tests covering export, CSS class, device name, badge, last-seen,
  HTML escaping, and null handling

muxplex/frontend/app.js

@@ -541,6 +541,37 @@ function buildAuthTileHTML(source) {
   );
 }
 
+/**
+ * Format a millisecond timestamp into a relative 'last seen' string.
+ * @param {number|null} ms - Millisecond timestamp
+ * @returns {string}
+ */
+function formatLastSeen(ms) {
+  if (ms == null) return 'Never';
+  var diff = Math.floor((Date.now() - ms) / 1000);
+  if (diff < 60) return diff + 's ago';
+  if (diff < 3600) return Math.floor(diff / 60) + 'm ago';
+  if (diff < 86400) return Math.floor(diff / 3600) + 'h ago';
+  return Math.floor(diff / 86400) + 'd ago';
+}
+
+/**
+ * Build the HTML string for an offline (unreachable) source tile.
+ * @param {{ name: string, url: string, lastSeenAt: number|null }} source
+ * @returns {string}
+ */
+function buildOfflineTileHTML(source) {
+  var escapedName = escapeHtml(source.name || '');
+  var lastSeen = formatLastSeen(source.lastSeenAt);
+  return (
+    '<article class="source-tile source-tile--offline">' +
+    '<span class="source-tile__name">' + escapedName + '</span>' +
+    '<span class="source-tile__badge">Offline</span>' +
+    '<span class="source-tile__last-seen">Last seen ' + escapeHtml(lastSeen) + '</span>' +
+    '</article>'
+  );
+}
+
 /**
  * Returns sessions with hidden session names removed.
  * Only hides LOCAL sessions (those with empty/absent sourceUrl) matching the
@@ -2219,6 +2250,8 @@ if (typeof module !== 'undefined' && module.exports) {
     renderFilterBar,
     // Federation tiles
     buildAuthTileHTML,
+    buildOfflineTileHTML,
+    formatLastSeen,
     // Test-only helpers
     _setCurrentSessions,
     _setViewMode,

muxplex/frontend/tests/test_app.mjs

@@ -2864,3 +2864,43 @@ test('buildAuthTileHTML escapes HTML in device name', () => {
   assert.ok(html.includes('<script>'), 'escaped script tag should appear in html');
 });
 
+// --- buildOfflineTileHTML ---
+
+test('buildOfflineTileHTML is exported as a function', () => {
+  assert.strictEqual(typeof app.buildOfflineTileHTML, 'function');
+});
+
+test('buildOfflineTileHTML returns article with source-tile--offline class', () => {
+  const html = app.buildOfflineTileHTML({ name: 'Dev Server', url: 'http://dev:8088', lastSeenAt: null });
+  assert.ok(html.startsWith('<article'), 'html should start with <article');
+  assert.ok(html.includes('source-tile--offline'), 'html should include source-tile--offline class');
+});
+
+test('buildOfflineTileHTML includes device name', () => {
+  const html = app.buildOfflineTileHTML({ name: 'Dev Server', url: 'http://dev:8088', lastSeenAt: null });
+  assert.ok(html.includes('Dev Server'), 'html should include the device name');
+});
+
+test('buildOfflineTileHTML includes Offline badge', () => {
+  const html = app.buildOfflineTileHTML({ name: 'Dev Server', url: 'http://dev:8088', lastSeenAt: null });
+  assert.ok(html.includes('Offline'), 'html should include Offline text');
+  assert.ok(html.includes('source-tile__badge'), 'html should include source-tile__badge class');
+});
+
+test('buildOfflineTileHTML shows relative last-seen time', () => {
+  const fiveMinAgo = Date.now() - 5 * 60 * 1000;
+  const html = app.buildOfflineTileHTML({ name: 'Dev Server', url: 'http://dev:8088', lastSeenAt: fiveMinAgo });
+  assert.ok(html.includes('Last seen'), 'html should include Last seen text');
+});
+
+test('buildOfflineTileHTML escapes device name', () => {
+  const html = app.buildOfflineTileHTML({ name: '<b>bad</b>', url: '', lastSeenAt: null });
+  assert.ok(!html.includes('<b>bad</b>'), 'raw <b>bad</b> must not appear in html');
+  assert.ok(html.includes('&lt;b&gt;bad&lt;/b&gt;'), 'device name should be HTML-escaped');
+});
+
+test('buildOfflineTileHTML shows "Never" when lastSeenAt is null', () => {
+  const html = app.buildOfflineTileHTML({ name: 'Dev Server', url: '', lastSeenAt: null });
+  assert.ok(html.includes('Never'), 'html should include Never when lastSeenAt is null');
+});
+