fix(plex): warm up HLS buffer on session start + player loading/buffering spinner

The Plex player stalled ~2s a few seconds into every auto-advanced next
episode. Root cause: each auto-advance spins up a cold ffmpeg HLS remux
session, and for a fresh start (start_s==0) start_session returned
immediately with zero buffer — hls.js drained the first segment, then
rebuffered waiting for the still-warming ffmpeg to write the next one.
Once ffmpeg gets ahead (stream-copy is faster than realtime) it never
stalls again.

- stream.py: before reporting a session ready, wait for the first
  _WARMUP_SEGMENTS (3) video segments to exist — the seg0 wait is now
  unconditional (was start_s>0 only) and warm-up runs for all starts.
  Best-effort and bounded: stop at the first segment not ready in time.
- PlexPlayer.tsx: a loading/buffering spinner. The existing overlay only
  covered the INITIAL load (!ready); add a `buffering` state driven by the
  video's waiting/stalled/seeking (set) and playing/canplay/seeked/pause
  (clear) events so a mid-playback stall or in-flight seek reads as
  "loading" instead of a frozen frame, and surface a fatal loadError even
  once playback has started. Spinner uses the shared Loader2.

Merges roadmap E6·item1 (spinner while loading/seeking) into this fix,
since the server-side warm-up deliberately holds ready a beat longer.

Tests: 3 new in test_plex_stream.py (warm-up waits for the first few
segments; stops at the first missing one; no warm-up when seg0 never
arrives). Gate: backend pytest 460 (Docker lane), FE tsc/lint/knip/
prettier + vitest 483.

backend/app/plex/stream.py

@@ -38,6 +38,17 @@ _HLS_ROOT = (
     else Path(settings.download_root) / ".plex-hls"
 )
 _SEG_SECONDS = 6
+# Cold-start warm-up. A freshly-spawned ffmpeg has produced only the first segment (or two) by the
+# time we could report the session ready; hls.js parses the EVENT playlist, drains that tiny buffer,
+# then STALLS a few seconds into playback waiting for the next segment the still-warming ffmpeg
+# hasn't written yet. Very visible on auto-advance to the next episode (start_s==0, which previously
+# returned with ZERO buffer). So before reporting ready we wait for the first few segments to exist:
+# the client then starts with ~_WARMUP_SEGMENTS×_SEG_SECONDS of buffer and, since stream-copy runs
+# faster than realtime, ffmpeg stays ahead from there and never stalls again. Best-effort and bounded
+# — we stop at the first segment that isn't ready within the per-segment budget (a slow miss is no
+# worse than the old zero-buffer behaviour).
+_WARMUP_SEGMENTS = 3
+_WARMUP_SEG_TIMEOUT_S = 8.0
 _SESSION_IDLE_S = 600  # reap a session with no access for this long
 # A session directory is named `{rating_key}_{int(start_s)}_{tag}_{aoff:+.2f}` (see start_session);
 # before multi-audio it was just `{rating_key}_{int(start_s)}`. `sweep_orphans` deletes ONLY names
@@ -296,16 +307,27 @@ def start_session(
         # Admin-configurable concurrency cap (Configuration → Plex → Max concurrent transcodes);
         # at least 1 so playback can't be capped to zero.
         _enforce_cap(max(1, sysconfig.get_int(db, "plex_max_transcodes")))
-    # Learn the REAL start offset K from the first VIDEO segment (outside the lock — this blocks on
-    # ffmpeg producing it, and we must not hold up other sessions). The client reads `media_start_s`, so
-    # its absolute clock + subtitle shift key off the true keyframe, not the requested offset. On
-    # timeout/probe failure we keep the provisional requested offset (old behaviour, small drift).
-    if start_s > 0:
-        seg0 = directory / ("seg_0_0.ts" if is_multi else "seg_0.ts")  # multi: video variant = v0
-        if wait_for(seg0, timeout=25.0):
-            k = _probe_first_pts(seg0)
+
+    # Wait for the first video segment, then warm up a few more — all outside the lock (this blocks on
+    # ffmpeg producing them, and we must not hold up other sessions).
+    def _seg(i: int) -> Path:
+        # multi-audio: the video rendition is variant v0 → seg_{i}_0.ts; single-audio → seg_{i}.ts
+        return directory / (f"seg_{i}_0.ts" if is_multi else f"seg_{i}.ts")
+
+    if wait_for(_seg(0), timeout=25.0):
+        # For a seek (start_s>0) learn the REAL start offset K from the first segment's absolute PTS,
+        # so the client's absolute clock + subtitle shift key off the true keyframe, not the requested
+        # offset. On probe failure we keep the provisional requested offset (old behaviour, small drift).
+        if start_s > 0:
+            k = _probe_first_pts(_seg(0))
             if k is not None and k >= 0:
                 s.media_start_s = k
+        # Warm up the buffer (see _WARMUP_SEGMENTS) so the client doesn't outrun the cold ffmpeg. Stop
+        # at the first segment that isn't ready in time — ffmpeg produces them faster than realtime once
+        # warm, so a miss means something slow and we proceed rather than block the request further.
+        for i in range(1, _WARMUP_SEGMENTS):
+            if not wait_for(_seg(i), timeout=_WARMUP_SEG_TIMEOUT_S):
+                break
     log.info(
         "plex hls session start key=%s req=%.1f real=%.3f multi=%s audio=%s",
         key,