feat(plex): field-scoped search (S2) + instant search typeahead

Add a search scope-pill to the Plex header search box (GitHub-style, one
field-scope at a time) and an instant typeahead of the top matches below it.

Backend (unified_library):
- New `field` param: all | title | people | summary | episode. `all` is
  byte-identical to the pre-scope behaviour (untouched weighted search_vector);
  a specific field keeps the GIN `search_vector @@ tsq` prefilter AND ANDs a
  per-column tsvector recheck, so scoped hits are a strict subset of Everywhere.
  Per-field expressions mirror the search_vector Computed def (same TS config,
  same left(summary,1000) truncation).
- `episode` scope empties the movie/show grid and title-only-matches the grouped
  Episodes section; the title/people/summary scopes suppress that section.
- Unknown field falls back to `all`. New DB-lane characterization tests
  (test_plex_field_scoped_search.py): each scope narrows correctly, field=all is
  identical to today, episode empties the grid and needs shows in scope.

Frontend:
- PlexSearchBox wraps the shared SearchBar with the scope-pill (reusing
  ActionMenu) and the typeahead; SearchBar gains generic leading/below/focus/
  keydown slots so other modules' search boxes are untouched.
- Episode scope offered only when shows are in scope (movie-only hides it),
  healed at the point of use like the sort state.
- Typeahead reuses /api/plex/library (limit=10), honours scope+field (not the
  sidebar filters), shows poster+title+year, keyboard nav (arrows/Enter/Esc),
  and jumps straight to a movie's info page or a show's drill-down via a new
  provider jumpTo hand-off (mirrors the playlistOpen pattern).
- `field` persisted per-account; en/hu labels added.

frontend/src/components/PlexProvider.tsx

@@ -1,6 +1,7 @@
 import { createContext, useCallback, useContext, useMemo, useState, type ReactNode } from "react";
 import { EMPTY_PLEX_FILTERS, type PlexFilters } from "../lib/api";
 import { parseSortState, type SortState } from "../lib/columnSort";
+import { parsePlexField, type PlexSearchField } from "../lib/plexSearch";
 import { PLEX_SORT_FALLBACK } from "../lib/plexSort";
 import { getAccountRaw, LS, setAccountRaw } from "../lib/storage";
 import { useAccountRehydrate } from "../lib/useAccountRehydrate";
@@ -19,13 +20,19 @@ import { useAccountRehydrate } from "../lib/useAccountRehydrate";
 // search term is deliberately its OWN state, NOT the feed's `filters.q`, so a Plex search never leaks
 // into (and is never greeted by a stale value from) the feed.
 
+// A "jump straight to this title" hand-off from the header typeahead: PlexBrowse opens a movie's
+// info page (like the card's ⓘ) or a show's drill-down (like clicking a show card) by type.
+export type PlexJumpTarget = { id: string; type: "movie" | "show" };
+
 type PlexState = {
   scope: string; // movie | show | both (unified cross-library scope)
   show: string;
   sort: SortState; // {key,dir}; healed against the scope's options at the point of use
   filters: PlexFilters;
   q: string;
+  field: PlexSearchField; // search scope-pill; healed against `scope` at the point of use
   playlistOpen: number | null;
+  jumpTo: PlexJumpTarget | null; // typeahead → grid hand-off ("open this title")
 };
 
 interface PlexActions {
@@ -34,7 +41,9 @@ interface PlexActions {
   setSort: (v: SortState) => void;
   setFilters: (f: PlexFilters) => void;
   setQ: (q: string) => void;
+  setField: (f: PlexSearchField) => void;
   setPlaylistOpen: (id: number | null) => void;
+  setJumpTo: (t: PlexJumpTarget | null) => void;
 }
 
 const StateContext = createContext<PlexState>({
@@ -43,7 +52,9 @@ const StateContext = createContext<PlexState>({
   sort: PLEX_SORT_FALLBACK,
   filters: EMPTY_PLEX_FILTERS,
   q: "",
+  field: "all",
   playlistOpen: null,
+  jumpTo: null,
 });
 const ActionsContext = createContext<PlexActions>({
   setScope: () => {},
@@ -51,7 +62,9 @@ const ActionsContext = createContext<PlexActions>({
   setSort: () => {},
   setFilters: () => {},
   setQ: () => {},
+  setField: () => {},
   setPlaylistOpen: () => {},
+  setJumpTo: () => {},
 });
 
 export function usePlex(): PlexState {
@@ -69,6 +82,7 @@ function readPlexScope(): string {
 const readPlexShow = (): string => getAccountRaw(LS.plexShow) ?? "all";
 const readPlexFiltersRaw = (): string => getAccountRaw(LS.plexFilters) ?? "{}";
 const readPlexQ = (): string => getAccountRaw(LS.plexQ) ?? "";
+const readPlexField = (): PlexSearchField => parsePlexField(getAccountRaw(LS.plexField));
 // Sort is a {key,dir} SortState. Migrate the old shape: a legacy bare-key string in plexSort plus the
 // direction that used to live in plexFilters.sortDir — so an existing sort preference survives the
 // upgrade rather than snapping back to the default.
@@ -118,7 +132,11 @@ export function PlexProvider({ children }: { children: ReactNode }) {
   }, [filtersRaw]);
   // Survives F5 (persisted), unlike the feed search — see the scope note above.
   const [q, setQState] = useState<string>(readPlexQ);
+  const [field, setFieldState] = useState<PlexSearchField>(readPlexField);
   const [playlistOpen, setPlaylistOpen] = useState<number | null>(null);
+  // Ephemeral hand-off like `playlistOpen`: the header typeahead sets the title to jump to;
+  // PlexBrowse consumes it into an info/show history subview then clears it.
+  const [jumpTo, setJumpTo] = useState<PlexJumpTarget | null>(null);
 
   // Re-read every per-account slice once the account is pinned after mount (first load on a fresh tab).
   const markDirty = useAccountRehydrate(() => {
@@ -127,6 +145,7 @@ export function PlexProvider({ children }: { children: ReactNode }) {
     setSortState(readPlexSort());
     setFiltersRaw(readPlexFiltersRaw());
     setQState(readPlexQ());
+    setFieldState(readPlexField());
   });
 
   const setScope = useCallback(
@@ -170,14 +189,22 @@ export function PlexProvider({ children }: { children: ReactNode }) {
     },
     [markDirty],
   );
+  const setField = useCallback(
+    (v: PlexSearchField) => {
+      markDirty();
+      setFieldState(v);
+      setAccountRaw(LS.plexField, v);
+    },
+    [markDirty],
+  );
 
   const state = useMemo<PlexState>(
-    () => ({ scope, show, sort, filters, q, playlistOpen }),
-    [scope, show, sort, filters, q, playlistOpen],
+    () => ({ scope, show, sort, filters, q, field, playlistOpen, jumpTo }),
+    [scope, show, sort, filters, q, field, playlistOpen, jumpTo],
   );
   const actions = useMemo<PlexActions>(
-    () => ({ setScope, setShow, setSort, setFilters, setQ, setPlaylistOpen }),
-    [setScope, setShow, setSort, setFilters, setQ],
+    () => ({ setScope, setShow, setSort, setFilters, setQ, setField, setPlaylistOpen, setJumpTo }),
+    [setScope, setShow, setSort, setFilters, setQ, setField],
   );
 
   return (