perf(plex): a card fetches its picture at a card's size, not the detail page's

Cards fetched the full cuts: a 400x600 poster (~38 KB) for a ~144px picture and the 1280x720
backdrop (~162 KB) for a ~212px shelf picture. The image proxy now also cuts thumb_sm (240x360)
and art_sm (480x270), cached apart; card pictures (grid, shelves, collection tiles, Up next) carry
both in srcset with sizes=auto, so the browser picks by laid-out width and DPR. Localdev:
17 KB a poster, 56 KB a backdrop. The detail page keeps the full cuts.

backend/app/plex/imgcache.py

@@ -23,9 +23,22 @@ log = logs.get_logger(__name__)
 
 _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.
-SIZES = {"thumb": (400, 600), "art": (1280, 720)}
+# Target box per variant — Plex resizes to these server-side. The full poster (400px) covers a detail
+# page's ≤224px poster at 2× DPR, the full art (1280px) a hero backdrop. A card is much smaller: a grid
+# poster is ~144px and a shelf's landscape art ~212px, so the `_sm` pair serves those at 1.33× DPR
+# (E31 S4e: cards fetched the 400 poster, 42 KB, and the 1280 art for a 212px picture). The browser
+# picks between a pair itself (`srcset`, the frontend's `plexSrcSet`).
+SIZES = {
+    "thumb": (400, 600),
+    "thumb_sm": (240, 360),
+    "art": (1280, 720),
+    "art_sm": (480, 270),
+}
+
+
+def picture(variant: str) -> str:
+    """Which stored picture a size variant is cut from: the poster (`thumb`) or the backdrop (`art`)."""
+    return "art" if variant.startswith("art") else "thumb"
 
 
 def key_for(db: Session, rating_key: str, variant: str) -> str | None: