feat(design): a page's background menu on the five list pages (E28 S3e4c)

A right-click on the EMPTY area of a page opens a menu of that page's own
toolbar: the feed (sort, reshuffle, view, watch state, content, source, clear
filters), the Plex library grid (sort, watch state, clear), the channel manager
(layout, the cards' sort, sync status, edit tags, clear the tag filter, read
subscriptions), a playlist (play all, group by, reset view, save order,
undo/redo, the list's own menu) and the notification center (mark all read).
No destructive row and no backfill.

PageShell listens on the page area; lib/backgroundTarget decides empty (not
text, a control, a link, media, or a row/card with its own menu). Shift+right-
click, a touch long-press and a right-click on selected words keep the
browser's menu. ui/PageMenu registers while mounted, so a loading or error
state keeps the browser's menu too. The rows mirror each control through
ui/pageMenuItems (sortSubmenu via pickSort, choiceSubmenu, multiSubmenu).
pageMenuScope.contract.test.ts pins the five pages.

frontend/src/components/PlexBrowse.tsx

@@ -30,6 +30,9 @@ import FilterSelect from "./ui/FilterSelect";
 import PlexDiscover from "./PlexDiscover";
 import { PlexCollectionsBrowse, PlexPlaylistsBrowse } from "./plexBrowseLists";
 import { PageToolbar } from "./ui/PageShell";
+import { PageMenu } from "./ui/PageMenu";
+import { menuGroups } from "./ui/menuGroups";
+import { choiceSubmenu, sortSubmenu } from "./ui/pageMenuItems";
 import ActiveFilterChips from "./ActiveFilterChips";
 import SelectedViewChip from "./SelectedViewChip";
 import ItemCount from "./ui/ItemCount";
@@ -531,8 +534,35 @@ export default function PlexBrowse() {
     );
   }
 
+  const showOptions = SHOW_OPTS.map((s) => ({ value: s, label: t(`plex.filter.showOpt.${s}`) }));
+  // The page's background menu (DESIGN "Background menu"): the toolbar's own controls, no more.
+  const pageMenuItems = menuGroups(
+    [
+      sortSubmenu({
+        id: "sort",
+        label: t("plex.filter.sort"),
+        options: sortOptions,
+        sort: sortState,
+        onChange: (next) => setSort(next ?? PLEX_SORT_FALLBACK),
+        ascLabel: t("plex.filter.dir.asc"),
+        descLabel: t("plex.filter.dir.desc"),
+      }),
+      choiceSubmenu({
+        id: "show",
+        label: t("plex.filter.show"),
+        options: showOptions,
+        selected: show,
+        onPick: setShow,
+      }),
+    ],
+    plexChips.length > 0
+      ? [{ id: "clear", label: t("sidebar.clearAll"), onSelect: clearAllFilters }]
+      : [],
+  );
+
   return (
     <div className="p-4 max-w-400 mx-auto">
+      <PageMenu ariaLabel={t("common.pageMenu")} items={pageMenuItems} />
       {/* The title count is fixed chrome — it portals into the shell's fixed band so it stays put
           while only the poster grid scrolls. */}
       <PageToolbar>
@@ -546,7 +576,7 @@ export default function PlexBrowse() {
               <FilterSelect
                 label={t("plex.filter.show")}
                 testId="plex-show"
-                options={SHOW_OPTS.map((s) => ({ value: s, label: t(`plex.filter.showOpt.${s}`) }))}
+                options={showOptions}
                 selected={[show]}
                 onChange={(next) => setShow(next[0] ?? "all")}
               />