fix(plex): give the library search its own ephemeral state

The Plex library search box wrote to the shared, persisted feed filter
(filters.q). That leaked a Plex query into the feed search box and, being
persisted, restored a stale query after a reload — which then collided
with a persisted collection filter to produce a confusing empty grid.
Plex now has its own search state: kept across page switches within a
session, but not persisted and not shared with the feed, so a reload
starts clean.

frontend/src/App.tsx

@@ -260,6 +260,12 @@ export default function App() {
     }
   }, [plexFiltersRaw]);
   const setPlexFilters = (f: PlexFilters) => setPlexFiltersRaw(JSON.stringify(f));
+  // The Plex library search term is its OWN ephemeral state — deliberately NOT the persisted feed
+  // `filters.q`. Sharing that box meant a Plex search leaked into the feed and, being persisted,
+  // greeted you with a stale query (colliding with a persisted collection filter → confusing
+  // "0 matches") after a reload. Kept in App so it survives page switches within a session, but
+  // resets on reload.
+  const [plexQ, setPlexQ] = useState("");
   // Bumped to tell the channel manager to drop a stale column filter when we send the user
   // there to see a specific set (the header's "without full history" link).
   const [channelsFilterReset, setChannelsFilterReset] = useState(0);
@@ -767,6 +773,8 @@ export default function App() {
           me={meQuery.data!}
           filters={filters}
           setFilters={setFilters}
+          plexQ={plexQ}
+          setPlexQ={setPlexQ}
           page={page}
           onYtSearch={enterYtSearch}
         />
@@ -819,8 +827,8 @@ export default function App() {
             />
           ) : page === "plex" && meQuery.data!.plex_enabled ? (
             <PlexBrowse
-              q={filters.q}
-              onClearSearch={() => setFilters({ ...filters, q: "" })}
+              q={plexQ}
+              onClearSearch={() => setPlexQ("")}
               library={plexLib}
               show={plexShowFilter}
               sort={plexSort}