refactor(frontend): each page fills the floating header itself; the header knows no page

The header used to pick its pills by `page === …` and import five module controls, and Plex's
Discover/Browse toggle needed a context bridge to reach the sub-view that lives in PlexBrowse.
Now the header is an empty band: PageShell hands its root box out as a slot, a page portals its
own pills into it (PageHeader), and the palette's Jump-to pill shows where no page does
(PageHeaderDefault, rendered inside the page's Suspense so a loading page shows no stand-in).
Plex's toggles take the sub-view as a prop; PlexViewBridge and its context are gone, and with
them the header's five layer suppressions.

No visible change: every header pill's box measured identical against the previous build on eight
pages, in Hungarian and English.

frontend/src/shell/App.tsx

@@ -37,7 +37,8 @@ import SetupWizard from "./SetupWizard";
 import Header from "./Header";
 import NavSidebar from "./NavSidebar";
 import BackToTop from "../components/ui/BackToTop";
-import PageShell from "../components/ui/PageShell";
+import PageShell, { PageHeaderDefault } from "../components/ui/PageShell";
+import { PaletteLauncher } from "../features/header/PaletteLauncher";
 import { SkipLink } from "../components/ui/SkipLink";
 import { pageTitleKey } from "../lib/pageMeta";
 import DebugRecorder from "../features/diagnostics/DebugRecorder";
@@ -68,7 +69,7 @@ const ReleaseNotes = lazy(() => import("./ReleaseNotes"));
 export default function App() {
   const { t, i18n } = useTranslation();
   const { page, channelView, ytSearch } = useNavigation();
-  const { setPage, enterYtSearch } = useNavigationActions();
+  const { setPage } = useNavigationActions();
   // An emailed verification link is confirmed HERE, above the signed-in/signed-out branch below, so
   // it works in a browser that already holds a session. It used to be handled inside Welcome, which
   // that branch never renders when signed in — the token was silently dropped. Signed out, the
@@ -452,7 +453,7 @@ export default function App() {
             title={t(pageTitleKey(page))}
             scrollKey={normalScrollKey}
             maxWidth={maxWidth}
-            header={<Header me={me!} onYtSearch={enterYtSearch} />}
+            header={<Header />}
             banners={
               <>
                 <VerifyBanner entry={verifyEntry} />
@@ -462,6 +463,9 @@ export default function App() {
           >
             <Suspense fallback={pageFallback}>
               <PageContent />
+              <PageHeaderDefault>
+                <PaletteLauncher />
+              </PageHeaderDefault>
             </Suspense>
           </PageShell>
         )}