fix(qbittorrent): reuse authenticated client across widget fetches

QbittorrentWidgetSource built a brand-new QbittorrentClient on every fetch,
logging in each time. With three qBittorrent widgets polling every 5-30s and
qBittorrent verifying passwords with slow PBKDF2 hashing, the concurrent login
load saturates its web thread pool and the reverse proxy returns 504 gateway
timeouts on /api/v2/auth/login. The client was already designed for reuse
(login once, SID cookie reuse, 403 re-login) — the source just wasn't using it.

Cache one QbittorrentClient per service (lru_cache keyed by service id, URL,
credentials, timeout) so the SID cookie persists across fetches and login
happens once. Mirrors dependencies._jellyfin_client_for. A credentials/URL
change produces a new cache key, so stale clients aren't reused after
reconfiguration.

Also surface 502/503/504 from the login as a clear "reverse proxy returned
HTTP <code> ... qBittorrent may be down/starting/overloaded" RuntimeError
instead of a bare HTTPError, so future gateway issues read as infrastructure,
not auth.

Tests: autouse fixture clears the client cache between tests; new gateway-error
login test. 385/385 backend tests pass; ruff clean.

backend/src/media_library_viewer_api/clients/.pi-map.index.md

@@ -2,7 +2,7 @@
 dir: backend/src/media_library_viewer_api/clients
 
 ## role
-Provides external service integration layer with read-only API client wrappers and remote/local execution helpers for aggregating data from media, directory, torrent, and authentication services.
+Provides external service integration clients (API wrappers and command executors) for media servers, identity providers, torrent clients, and remote/local filesystems.
 ## parent
 index: backend/src/media_library_viewer_api/.pi-map.index.md
 map: backend/src/media_library_viewer_api/.pi-map.md