fix(plex): image proxy no longer exhausts the DB connection pool

A collections page fires 100+ concurrent poster requests. Both image proxies
(/image and /person-image) authenticated via current_user + Depends(get_db),
holding a pooled DB connection for the whole request — including the slow Plex/
CDN fetch. Under the burst, the 15-connection pool was exhausted → QueuePool
checkout timeouts → 502s → slow, partially-loaded grids on prod.

Fix: authenticate these two high-fan-out endpoints with a signed-session check
(no DB user-load), serve disk-cache hits with zero DB access, and on a cold miss
open a short session only to resolve the image key + Plex config, releasing it
BEFORE the fetch (image_bytes uses no DB). Also raise the pool (20 + 30 overflow)
as headroom above the sync-endpoint threadpool.

backend/app/db.py

@@ -10,7 +10,17 @@ class Base(DeclarativeBase):
     pass
 
 
-engine = create_engine(settings.database_url, pool_pre_ping=True, future=True)
+# Pool sized above the sync-endpoint threadpool (~40) so a burst of short DB sessions can't starve on
+# checkout. The image proxies deliberately DON'T hold a connection during their slow external fetch
+# (see routes/plex.py), so this headroom is only for the many brief sessions, not long ones.
+engine = create_engine(
+    settings.database_url,
+    pool_pre_ping=True,
+    pool_size=20,
+    max_overflow=30,
+    pool_timeout=30,
+    future=True,
+)
 SessionLocal = sessionmaker(bind=engine, autoflush=False, expire_on_commit=False)