improvement(plex): serve right-sized poster/art images via Plex transcode

Posters/art were proxied at full resolution (many 1-7MB, some 9.5MB) into ≤176px
grid/info cells — heavy to fetch + decode, so fast scrolling lagged 1-2s even
with a warm cache (the cache removed the Plex round-trip, not the image weight).

Now PlexClient.image_bytes optionally hits Plex's /photo/:/transcode to resize
server-side; the /image endpoint requests thumb=400x600, art=1280x720 and keys
the cache by width (old full-size files orphaned, re-cached small). Measured:
a poster 5.5MB->50KB, art 8.1MB->137KB, at 400x600 (crisp on 2x DPR). Grid
scroll is near-instant and the disk cache shrinks ~8x.

backend/app/routes/plex.py

@@ -534,6 +534,9 @@ def _image_key(db: Session, rating_key: str, variant: str) -> str | None:
 _IMG_CACHE = Path(settings.download_root) / ".plex-img-cache"
 _EXT_CT = [("jpg", "image/jpeg"), ("png", "image/png"), ("webp", "image/webp")]
 _CT_EXT = {ct: ext for ext, ct in _EXT_CT}
+# Target box per variant — Plex resizes to these server-side. Posters fill ≤176px cells (grid/info/
+# strips), so 400px covers 2× DPR; the faint backdrop art only needs ~1280px. Keeps images ~tens of KB.
+_IMG_SIZES = {"thumb": (400, 600), "art": (1280, 720)}
 
 
 def _img_cache_read(key: str) -> tuple[bytes, str] | None:
@@ -584,7 +587,11 @@ def image(rating_key: str, request: Request, variant: str = "thumb") -> Response
     fetch. Auth is the signed-session check (no DB user-load)."""
     _require_session(request)
     v = "art" if variant == "art" else "thumb"
-    cache_key = f"item_{rating_key}_{v}"
+    w, h = _IMG_SIZES[v]
+    # Size is part of the cache key: Plex resizes server-side (see PlexClient.image_bytes), so we cache
+    # the small variant. The width tag also means changing a target size just re-caches, never serves a
+    # stale differently-sized file (old full-size files under the un-tagged key are simply orphaned).
+    cache_key = f"item_{rating_key}_{v}_{w}"
     hit = _img_cache_read(cache_key)
     if hit:
         return _img_response(*hit)
@@ -599,7 +606,7 @@ def image(rating_key: str, request: Request, variant: str = "thumb") -> Response
         raise HTTPException(status_code=400, detail=str(e))
     try:
         with plex:
-            data, ct = plex.image_bytes(key)
+            data, ct = plex.image_bytes(key, w, h)
     except PlexError as e:
         raise HTTPException(status_code=502, detail=f"Plex image fetch failed: {e}")
     _img_cache_write(cache_key, data, ct)