refactor(plex): address /code-review on the R12 S1 split

Cleanup only, no behaviour change (ruff clean + pytest 193):
- imports hoisted above `router =` and grouped/sorted (isort) across the split
  files; ruff-format pass restores the 2-blank-line PEP8 spacing the generator
  collapsed to 1.
- the shared on-disk cache root moves to a neutral app/plex/cache.py, so
  subtitles.py no longer imports it from imgcache.py (drops the cross-import).
- the former plex.py module docstring's access-model note (read endpoints open
  to any authed user; admin endpoints test/sync) is restored in the package
  __init__.py.

backend/app/plex/imgcache.py

@@ -5,18 +5,15 @@ LAN (janky). We cache the fetched bytes on local disk keyed by a stable id, so r
 other users) serve instantly from disk. On-demand + bounded by the library size; no eviction (a
 few hundred MB at most for a big library — acceptable, matching the download disk trade-offs).
 
-`CACHE_DIR` is the shared Plex on-disk cache root; converted subtitle VTTs live here too
-(see ``subtitles.py``).
+The cache directory (``cache.CACHE_DIR``) is shared with the subtitle cache (see ``subtitles.py``).
 """
-from pathlib import Path
 
 from fastapi import Response
 from sqlalchemy.orm import Session
 
-from app.config import settings
 from app.models import PlexCollection, PlexItem, PlexSeason, PlexShow
+from app.plex.cache import CACHE_DIR
 
-CACHE_DIR = 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/
@@ -65,4 +62,6 @@ def write(key: str, data: bytes, ct: str) -> None:
 
 
 def response(data: bytes, ct: str) -> Response:
-    return Response(content=data, media_type=ct, headers={"Cache-Control": "public, max-age=86400"})
+    return Response(
+        content=data, media_type=ct, headers={"Cache-Control": "public, max-age=86400"}
+    )