feat(header): move the sync status into a chip on the header

The rail spent a two-row block plus a divider on per-user sync status. It's
global, not per-module, so it now rides the right end of the floating header as
a pill: the headline count at a glance, an accent dot when something wants you
(paused / missing history), and the counts, state, the channel-manager link and
pause in a popover.

Frees the rail's whole top block. Also drops SyncStatus's two now-dead layouts:
"bar" was a leftover of the top bar removed in 0.42.0, and "rail" lost its only
caller here — the component is chip-only, ~60 lines lighter, and the popover
reuses useDismiss.

frontend/src/components/Header.tsx

@@ -6,11 +6,11 @@ import type { Page } from "../lib/urlState";
 import { moduleLabelKey, moduleOrder, stepModule } from "../lib/modules";
 import ModuleName from "./ModuleName";
 import SearchBar from "./SearchBar";
+import SyncStatus from "./SyncStatus";
 
-// The floating top header: a fixed-position row of glass pills over the content — a ModuleName
-// pill (label + accent dot + back/forward arrows) and, where a module searches, a SearchBar pill.
-// The row's left edge is a constant (as if the nav rail AND filter sidebar were both open), so it
-// never shifts when either collapses or when paging between modules; the right edge leaves ~10%.
+// The floating top header: a row of glass pills over the content — a ModuleName pill (label +
+// accent dot + back/forward arrows), the module's SearchBar where it has one, and the per-user
+// sync chip at the right end.
 export default function Header({
   me,
   filters,
@@ -24,6 +24,7 @@ export default function Header({
   page,
   setPage,
   onYtSearch,
+  onGoToFullHistory,
 }: {
   me: Me;
   filters: FeedFilters;
@@ -40,6 +41,8 @@ export default function Header({
   // Trigger a live YouTube search for the current term (feed only; hidden for the demo account,
   // which can't spend the shared quota).
   onYtSearch: (q: string) => void;
+  // Jump to the channel manager filtered to channels still missing full history.
+  onGoToFullHistory: () => void;
 }) {
   const { t } = useTranslation();
   // The ◀/▶ arrows step cyclically through the user's available modules (derived from `me`, so
@@ -116,6 +119,11 @@ export default function Header({
         canNext={multiModule}
       />
       {search}
+      {/* Per-user sync status — global, not per-module, so it rides the right end of the header
+          rather than costing the nav rail a whole block. */}
+      <div className="ml-auto">
+        <SyncStatus isAdmin={me.role === "admin"} onGoToFullHistory={onGoToFullHistory} />
+      </div>
     </div>
   );
 }