refactor(player): the Plex session machine is a tested engine, one request per item in flight

PlexPlayer's session logic (generation, pending play intent, clock ownership, session offset, reclaim
budget, listener teardown) moves into lib/hlsEngine.ts, a plain class with hls.js behind lib/hlsPort.ts
and its own unit tests.

- A seek, track change or reclaim asked for while a session request is out replaces the queued
  target; it is sent once the in-flight answer settles. A burst of 20 presses past the buffer was 20
  requests and 20 ffmpeg spawns; it is now 2-3, and plays again ~2 s sooner.
- The player stops its server session when it leaves the item, closes or the page unloads
  (POST /api/plex/stream/{rk}/session/{sid}/stop, identity-aware). A left transcode used to run to
  the end of the film first.
- A restart asked for after a new session attached but before it played no longer reads the emptied
  media as the viewer's pause.

backend/app/routes/plex/playback.py

@@ -637,12 +637,27 @@ def stream_session(
         # The session id is part of the path (not a query param) so the playlist's RELATIVE segment
         # names resolve back into the same session — see `stream_hls_file` for why it has to.
         "url": f"/api/plex/stream/{it.rating_key}/hls/{s.id}/{s.entry}",
+        # What the player names when it no longer wants the session (POST …/session/{id}/stop).
+        "id": s.id,
         "transcode": s.transcode,
         "hw": s.hw,
         "tonemap": s.tonemap,
     }
 
 
+@router.post("/stream/{rating_key}/session/{session_id}/stop")
+def stream_session_stop(
+    rating_key: str,
+    session_id: str,
+    user: User = Depends(current_user),
+) -> dict:
+    """The player no longer wants this session (it left the item, closed, or the page unloaded):
+    its ffmpeg stops now instead of at the idle reaper. A POST, so the player can send it as a
+    keepalive beacon from a page being unloaded. Stops nothing but the caller's own session, and
+    only while it is still the one registered for the item (see `stop_session`)."""
+    return {"ok": True, "stopped": plex_stream.stop_session(user.id, rating_key, session_id)}
+
+
 @router.get("/stream/{rating_key}/file")
 def stream_file(
     rating_key: str,