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/subtitles.py

@@ -2,22 +2,33 @@
 
 Text subtitles (embedded or external) are turned into WebVTT so the browser <track> can render them;
 bitmap subtitles (Blu-ray/DVD) can't be (would need burn-in). Converted VTTs are cached on the shared
-Plex on-disk cache root (``imgcache.CACHE_DIR``).
+Plex on-disk cache root (``cache.CACHE_DIR``).
 """
+
 import re
 import subprocess
 
+from app.plex.cache import CACHE_DIR
 from app.plex.client import PlexError
-from app.plex.imgcache import CACHE_DIR
 
 # Image-based subtitle codecs (Blu-ray/DVD) — can't be turned into text WebVTT (would need burn-in).
-BITMAP_SUBS = {"pgs", "hdmv_pgs_subtitle", "dvd_subtitle", "dvdsub", "vobsub", "dvbsub", "dvb_subtitle"}
+BITMAP_SUBS = {
+    "pgs",
+    "hdmv_pgs_subtitle",
+    "dvd_subtitle",
+    "dvdsub",
+    "vobsub",
+    "dvbsub",
+    "dvb_subtitle",
+}
 
 
 def srt_to_vtt(text: str) -> str:
     """Minimal SubRip→WebVTT: add the header and switch the ms separator (`,`→`.`). SRT cue-index
     lines are valid in WebVTT, so they're left as-is."""
-    body = re.sub(r"(\d\d:\d\d:\d\d),(\d\d\d)", r"\1.\2", text.replace("\r\n", "\n").lstrip(""))
+    body = re.sub(
+        r"(\d\d:\d\d:\d\d),(\d\d\d)", r"\1.\2", text.replace("\r\n", "\n").lstrip("")
+    )
     return "WEBVTT\n\n" + body.strip() + "\n"
 
 
@@ -75,7 +86,9 @@ def shift_vtt(vtt: str, offset: float) -> str:
             if en <= 0:
                 keep = False  # whole cue is before the session start → drop the block
             else:
-                lines[i] = f"{_vtt_s_to_ts(st)} --> {_vtt_s_to_ts(en)}{settings}"  # _vtt_s_to_ts clamps st>=0
+                lines[i] = (
+                    f"{_vtt_s_to_ts(st)} --> {_vtt_s_to_ts(en)}{settings}"  # _vtt_s_to_ts clamps st>=0
+                )
             break
         if keep:
             out_blocks.append("\n".join(lines))
@@ -85,11 +98,25 @@ def shift_vtt(vtt: str, offset: float) -> str:
 def ffmpeg_to_vtt(src: str, sub_ord: int | None) -> str:
     """Convert one subtitle stream of a file to WebVTT via ffmpeg (for embedded subs, and non-SRT
     external subs written to a temp file). `sub_ord` = ordinal among the file's subtitle streams."""
-    cmd = ["ffmpeg", "-nostdin", "-loglevel", "error", "-i", src,
-           "-map", f"0:s:{sub_ord if sub_ord is not None else 0}", "-f", "webvtt", "pipe:1"]
+    cmd = [
+        "ffmpeg",
+        "-nostdin",
+        "-loglevel",
+        "error",
+        "-i",
+        src,
+        "-map",
+        f"0:s:{sub_ord if sub_ord is not None else 0}",
+        "-f",
+        "webvtt",
+        "pipe:1",
+    ]
     r = subprocess.run(cmd, capture_output=True)
     if r.returncode != 0 or not r.stdout:
-        raise PlexError((r.stderr or b"").decode("utf-8", "replace")[:200] or "ffmpeg subtitle convert failed")
+        raise PlexError(
+            (r.stderr or b"").decode("utf-8", "replace")[:200]
+            or "ffmpeg subtitle convert failed"
+        )
     return r.stdout.decode("utf-8", "replace")