perf(plex): a card fetches its picture at a card's size, not the detail page's

Cards fetched the full cuts: a 400x600 poster (~38 KB) for a ~144px picture and the 1280x720
backdrop (~162 KB) for a ~212px shelf picture. The image proxy now also cuts thumb_sm (240x360)
and art_sm (480x270), cached apart; card pictures (grid, shelves, collection tiles, Up next) carry
both in srcset with sizes=auto, so the browser picks by laid-out width and DPR. Localdev:
17 KB a poster, 56 KB a backdrop. The detail page keeps the full cuts.

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

@@ -363,3 +363,19 @@ describe("PlexPosterCard on a shelf", () => {
     }
   });
 });
+
+// E31 S4e: a card fetched the detail page's 400px poster for its ~144px picture. It offers the
+// proxy's small cut too and lets the browser pick by its width.
+describe("a Plex card's picture", () => {
+  it("offers the small cut beside the full one, lazily", () => {
+    const { container } = render(
+      <PlexPosterCard card={{ ...movie(), thumb: "/api/plex/image/1" }} onOpen={vi.fn()} />,
+    );
+    const img = container.querySelector("img")!;
+    expect(img.getAttribute("srcset")).toBe(
+      "/api/plex/image/1?variant=thumb_sm 240w, /api/plex/image/1 400w",
+    );
+    expect(img.getAttribute("sizes")).toBe("auto, 200px");
+    expect(img.getAttribute("loading")).toBe("lazy");
+  });
+});