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.

backend/app/routes/plex/detail.py

@@ -14,6 +14,7 @@ from app.collation import collated, sorted_words
 from app import logs
 from app.auth import current_user
 from app.db import get_db
+from app.discover import queries
 from app.models import (
     PlexCollection,
     PlexItem,
@@ -221,6 +222,24 @@ def show_detail(
     }
 
 
+@router.get("/show/{rating_key}/next")
+def show_next(
+    rating_key: str,
+    lang: str = "en",
+    user: User = Depends(current_user),
+    db: Session = Depends(get_db),
+) -> dict:
+    """The episode a show's card plays: the one in progress, else the first unwatched, else the first
+    (`discover.queries.next_episode`, the rule Home's shelves and the show page's Resume follow).
+    Asked one show at a time, when a card is hovered or played, rather than carried on every card of a
+    grid: three probes a show would cost a 60-card page 180 queries for the few cards anyone plays.
+    `next` is null for a show with no episodes."""
+    sh = by_rating_key(db, PlexShow, rating_key)
+    if sh is None:
+        raise not_found("show")
+    return {"next": queries.next_episode(db, user.id, sh.id, lang=_norm_lang(lang))}
+
+
 def _season_block(se: PlexSeason, cards: list[dict]) -> dict:
     """A season's card for the show page (with its aggregate rollup) plus its episodes (used by the
     season subpage, read from the same cached show-detail payload)."""