feat(plex): every show card plays the episode it would put on

A show card's picture opened the show page everywhere but Home, whose shelves carried the
resolved `next`. Now every Plex picture plays: a show asks `GET /api/plex/show/{id}/next`
(the in-progress episode, else the first unwatched, else S1·E1 — the rule Home and the show
page's Resume follow) on the click, fresh each time. A started show shows Continue + Restart;
its title, an ⓘ and the menu's "Open show" row open its page; one with no episodes opens there.

The question is asked per show, never carried on every card: three probes a show would cost a
grid page up to 180 queries. The hover preview asks it once it opens and names the episode
("Next: S6·E16 — Title"). Related shows on a show page play the same way.

frontend/src/components/PlexBrowse.tsx

@@ -26,6 +26,7 @@ import { useDebounced } from "../lib/useDebounced";
 import { useHistorySubview } from "../lib/history";
 import { PLEX_SUB_URL, type Sub } from "./plexSubUrl";
 import { toggleWatchState } from "../lib/plexWatch";
+import { usePlayShow } from "./usePlayShow";
 import SortControl from "./ui/SortControl";
 import FilterSelect from "./ui/FilterSelect";
 import PlexDiscover from "./PlexDiscover";
@@ -328,13 +329,23 @@ export default function PlexBrowse() {
     return () => io.disconnect();
   }, [sentinelEl, hasNextPage, isFetching, fetchNextPage]);
 
+  const resolveShow = usePlayShow(
+    (id, fromStart) => sub.open({ kind: "player", id, fromStart }),
+    (id) => sub.open({ kind: "show", id }),
+  );
+  // A show's card plays the episode it resolves to (usePlayShow); the grid's place is kept first.
+  function playShow(card: PlexCard, fromStart: boolean) {
+    scrollRef.current = scroller()?.scrollTop ?? 0;
+    void resolveShow(card, fromStart);
+  }
   function onCard(card: PlexCard) {
+    if (card.type === "show") return playShow(card, false);
     scrollRef.current = scroller()?.scrollTop ?? 0; // remember grid position for the trip back
-    if (card.type === "show") sub.open({ kind: "show", id: card.id });
-    else sub.open({ kind: "player", id: card.id });
+    sub.open({ kind: "player", id: card.id });
   }
   // The started card's Restart (C5): the same trip, from 0 instead of the resume point.
   function onRestartCard(card: PlexCard) {
+    if (card.type === "show") return playShow(card, true);
     scrollRef.current = scroller()?.scrollTop ?? 0;
     sub.open({ kind: "player", id: card.id, fromStart: true });
   }
@@ -509,6 +520,7 @@ export default function PlexBrowse() {
         }
         onOpenSeason={(seasonId) => sub.open({ kind: "season", showId, seasonId })}
         onOpenShow={(id) => sub.open({ kind: "show", id })}
+        onPlayShow={playShow}
         onFilter={applyFilter}
         onOpenPerson={onOpenPerson}
       />