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/usePlexCardActions.tsx

@@ -17,8 +17,10 @@ import { type ActionMenuItem } from "./ui/ActionMenu";
 // the everyday toggles (watched, add to playlist) on hover; details, copy and the pin live here.
 
 export interface PlexActionHandlers {
+  /** Play it: a show, the episode it would play (the surface resolves it). */
   onOpen: (c: PlexCard) => void;
-  /** The media-info page. Omitted where a surface has none (the episode lists). */
+  /** The media-info page, or a show's own page. Omitted where a surface has none (the episode
+   *  lists). */
   onInfo?: (c: PlexCard) => void;
   onToggleWatched?: (c: PlexCard) => void;
   /** Play from the start instead of the resume point (C5). Where given, a started title lists it
@@ -32,7 +34,8 @@ const icon = "w-4 h-4";
 export const plexAddLabelKey = (c: PlexCard): string =>
   c.type === "episode" ? "plex.playlist.addEpisode" : "plex.playlistAdd.manage";
 
-/** A show opens its drill-down; a movie or an episode plays. */
+/** A leaf: a movie or an episode, what the watched toggle, the playlist add and a resume point
+ *  belong to. A show plays too, through the episode it resolves to. */
 const isPlexPlayable = (c: PlexCard): boolean => c.type !== "show";
 
 /** Has a resume point: the click continues it, and "from the start" is a choice. A watched item is
@@ -73,15 +76,17 @@ export function usePlexCardActions(handlers: PlexActionHandlers, open: boolean)
   ): ActionMenuItem[] => {
     const { onOpen, onInfo, onToggleWatched, onRestart } = handlers;
     const playable = isPlexPlayable(c);
+    const isShow = c.type === "show";
     const watched = c.status === "watched";
-    const started = plexStarted(c);
+    // A show continues where its rollup says it stands, as its card's Continue + Restart do.
+    const started = isShow ? c.status === "in_progress" : plexStarted(c);
     return [
       ...(play
         ? [
             {
               id: "play",
-              label: !playable ? t("plex.openShow") : started ? t("card.continue") : t("plex.play"),
-              icon: playable ? <Play className={icon} /> : <Tv2 className={icon} />,
+              label: started ? t("card.continue") : t("plex.play"),
+              icon: <Play className={icon} />,
               onSelect: () => onOpen(c),
             },
             // The same words and glyph as the video card's menu (useVideoActions).
@@ -131,18 +136,18 @@ export function usePlexCardActions(handlers: PlexActionHandlers, open: boolean)
             },
           ]
         : []),
-      ...(playable && onInfo
+      ...(onInfo
         ? [
             {
               id: "details",
-              label: t("plex.info.title"),
-              icon: <Info className={icon} />,
+              label: isShow ? t("plex.openShow") : t("plex.info.title"),
+              icon: isShow ? <Tv2 className={icon} /> : <Info className={icon} />,
               separatorBefore: true,
               onSelect: () => onInfo(c),
             },
           ]
         : []),
-      ...copy(c.title, null).map((it) => ({ ...it, separatorBefore: !(playable && onInfo) })),
+      ...copy(c.title, null).map((it) => ({ ...it, separatorBefore: !onInfo })),
       ...(withPin ? pin.item(pinPlex(c), c.title) : []),
     ];
   };