fix(api): progress checkpoints past the int4 column are a 422, and idle HLS sessions are reaped on a timer

Deep-review round 3 of bug hunt 2026-09.

- The YouTube and Plex progress bodies are bounded by POSITION_MAX_S (the int4 position columns): a
  finite position of 2^31 or more was a DataError, i.e. a 500 — the sibling of round 2's non-finite
  fix.
- plex/stream.py promised "a periodic reaper", but reap_idle ran only inside the NEXT session
  request: after the last playback an abandoned session (its ffmpeg still working, its directory a
  whole segmented copy of the film) lived until someone pressed play again. A lifespan task reaps
  every 60 s.
- Tests for what round 2 left untested: the 422's body keeps the list shape the UI localizes, and
  stream_session refuses non-finite start/aoff.

backend/app/main.py

@@ -81,6 +81,7 @@ async def lifespan(app: FastAPI):
     # alone doesn't buy that; not waiting does. The sweep only touches directories no live session
     # owns, so racing it against early playback is safe.
     sweep = asyncio.create_task(_sweep_hls_orphans())
+    reaper = asyncio.create_task(_reap_hls_sessions())
     start_scheduler()
     try:
         yield
@@ -90,15 +91,33 @@ async def lifespan(app: FastAPI):
         # pending ("Task was destroyed but it is pending!" — noise that reads like a bug during
         # triage). Cancelling does NOT interrupt the rmtree thread itself; this only makes our own
         # bookkeeping honest.
-        sweep.cancel()
-        with suppress(asyncio.CancelledError):
-            await sweep
+        for task in (sweep, reaper):
+            task.cancel()
+            with suppress(asyncio.CancelledError):
+                await task
         shutdown_scheduler()
         # Kills a running subtitle extraction: its worker would otherwise hold interpreter exit for
         # the rest of the read (see plex_subtitles.shutdown).
         plex_subtitles.shutdown()
 
 
+# How often idle HLS sessions are reaped (see plex/stream.py `reap_idle`).
+_HLS_REAP_EVERY_S = 60.0
+
+
+async def _reap_hls_sessions() -> None:
+    """The periodic reaper plex/stream.py's docstring promises. `reap_idle` used to run only inside
+    the NEXT session request, so after the last playback of the day an abandoned session — its
+    ffmpeg still working through the film, its directory a whole segmented copy of it — lived until
+    somebody pressed play again or the process restarted."""
+    while True:
+        await asyncio.sleep(_HLS_REAP_EVERY_S)
+        try:
+            await asyncio.to_thread(plex_stream.reap_idle)
+        except Exception:
+            log.exception("HLS session reap failed")
+
+
 async def _sweep_hls_orphans() -> None:
     """Background half of the startup HLS sweep (see lifespan). Owns its own errors: a failure here
     must never take the app down, and a cancelled shutdown is not one."""