fix(plex): a Surprise draw stays put until its reshuffle

The rail's query was always stale, so Back from a card's player or page remounted it into a new
draw, as did a return to the window: the card just looked at was gone. It now stands until the
reshuffle (or another scope, language or filter) asks for a new one.

frontend/src/components/PlexDiscover.dom.test.tsx

@@ -7,7 +7,7 @@
 // synchronously. The rails scroll inside a Carousel (useHScroll → ResizeObserver), stubbed for jsdom.
 import { describe, it, expect, afterEach, beforeAll, vi } from "vitest";
 import { act, render, screen, fireEvent, cleanup, waitFor } from "@testing-library/react";
-import { QueryClient, QueryClientProvider } from "@tanstack/react-query";
+import { focusManager, QueryClient, QueryClientProvider } from "@tanstack/react-query";
 
 beforeAll(() => {
   class Stub {
@@ -223,6 +223,37 @@ describe("PlexDiscover", () => {
     expect(plexSurprise.mock.calls[1]?.[4]).toEqual(["sp1"]);
   });
 
+  // Back from a card's player or page remounts the surface: the draw it left must still be there.
+  it("keeps its draw across a remount and a return to the window; only ↻ redraws", async () => {
+    plexDiscover.mockResolvedValue(fullPayload);
+    plexSurprise.mockResolvedValue({ scope: "both", items: [card("sp1", "Random Pick")] });
+    const qc = new QueryClient({ defaultOptions: { queries: { retry: false } } });
+    const ui = (
+      <QueryClientProvider client={qc}>
+        <PlexDiscover
+          scope="both"
+          onOpenCard={noop}
+          onRestartCard={() => {}}
+          onInfoCard={noop}
+          onGenre={noop}
+          onSeeAllRecent={noop}
+        />
+      </QueryClientProvider>
+    );
+    const first = render(ui);
+    await screen.findByText("Random Pick");
+    first.unmount();
+    render(ui);
+    await screen.findByText("Random Pick");
+    act(() => {
+      focusManager.setFocused(false);
+      focusManager.setFocused(true);
+    });
+    await new Promise((r) => setTimeout(r, 20));
+    expect(plexSurprise).toHaveBeenCalledTimes(1);
+    focusManager.setFocused(undefined);
+  });
+
   it("shows the empty message when every rail is empty", async () => {
     plexDiscover.mockResolvedValue({
       scope: "both",

frontend/src/components/PlexDiscover.tsx

@@ -134,7 +134,10 @@ export default function PlexDiscover({
         shown.map((c) => c.id),
       );
     },
-    staleTime: 0,
+    // A draw stands until ↻ (or another scope, language or filter) asks for a new one. A stale one was
+    // redrawn on every remount — Back from the player or a show page — and on a return to the window,
+    // so the card just looked at was gone from the rail it came from.
+    staleTime: Infinity,
   });
 
   // Watched toggle over BOTH this surface's cache (so a rail card flips instantly) and the surprise