fix(ui,plex): a dialog keeps the focus its child asked for, and a hopeless segment fails at once

Both found by UAT in a real browser, after the tests for them were already green — which is the
whole reason this repo settles focus and timing claims by running them.

- **The autoFocus fix worked, and then the dialog took the focus back.** React 18's StrictMode runs
  every effect mount→cleanup→mount in development: the cleanup handed focus back to the trigger, and
  the second mount, finding the focus outside the dialog, moved it to the first focusable — off the
  `autoFocus` field a beat after the browser had put it there. Chrome measured it: INPUT (commitMount)
  → BODY (cleanup) → ✕ (re-mount). The effect is idempotent now — it remembers what the dialog was
  focused on and restores THAT on a re-mount — and the close-time restore is conditional on the
  dialog still holding the focus, which it tracks as it changes rather than computing at cleanup,
  where the panel is already out of the document. A dialog no longer yanks focus back from wherever
  the user has since moved it.

- **Passing ffmpeg's handle to the segment wait only shortened the FINISHED case.** Measured against
  the running localdev API: a request for `seg_99999.ts` on a live session still took 20 195 ms,
  because that ffmpeg has not exited and the wait has no other reason to stop. ffmpeg writes segments
  in order, so a segment whose predecessor does not exist is not the next one and cannot arrive —
  and that is knowable at once. Same request now: 45 ms.

Verified on localdev against the real library (Westworld S01E06, remux, multi-audio): Mod+K opens the
command palette with the focus in its search field and typing reaches it; playback runs on the new
session-scoped HLS URL; a request naming a stale session id is a 404; and a viewer paused for longer
than the finished-session rule keeps their 2.4 GB session across two reaper passes — the progress
checkpoint touches it — and resumes cleanly.

vitest 1009, pytest 1127.

backend/tests/test_plex_hls_file_route.py

@@ -24,8 +24,11 @@ from app.plex import stream as plex_stream
 
 
 class _Proc:
+    def __init__(self, running: bool = False):
+        self.running = running
+
     def poll(self):
-        return 0  # finished: `wait_for` may not poll out its whole timeout on a missing file
+        return None if self.running else 0
 
     def terminate(self):
         pass
@@ -35,10 +38,10 @@ class _Proc:
 
 
 class _Session:
-    def __init__(self, session_id: str, directory):
+    def __init__(self, session_id: str, directory, running: bool = False):
         self.id = session_id
         self.dir = directory
-        self.proc = _Proc()
+        self.proc = _Proc(running)
         self.last_access = time.time()
 
 
@@ -75,6 +78,7 @@ def _client(db, monkeypatch):
 def test_a_segment_is_served_from_the_session_the_url_names(db, monkeypatch, tmp_path, sessions):
     d = tmp_path / "m1_0_0_+0.00"
     d.mkdir()
+    (d / "seg_11.ts").write_bytes(b"")  # its predecessor, so seg_12 is the next one
     (d / "seg_12.ts").write_bytes(b"mine")
     sessions["m1"] = _Session("sid-a", d)
     client = _client(db, monkeypatch)
@@ -93,6 +97,7 @@ def test_a_segment_of_a_replaced_session_is_a_404_not_the_new_sessions_bytes(
     next segment must fail honestly — the player reclaims at the playhead — not arrive as B's."""
     theirs = tmp_path / "m1_1500_0_+0.00"
     theirs.mkdir()
+    (theirs / "seg_11.ts").write_bytes(b"")
     (theirs / "seg_12.ts").write_bytes(b"theirs")
     sessions["m1"] = _Session("sid-b", theirs)
     client = _client(db, monkeypatch)
@@ -127,12 +132,15 @@ def test_a_playlist_with_no_live_session_is_a_404_not_a_silent_restart_at_zero(
 
 def test_a_segment_that_will_never_arrive_fails_at_once(db, monkeypatch, tmp_path, sessions):
     """`stream_hls_file` is a SYNC route: it runs on the ~40-slot threadpool and holds a pooled DB
-    connection while it waits. Waiting without the producer's handle polled out the whole 20 s even
-    when that ffmpeg had already exited and no segment could ever appear — one ordinary seek past the
-    produced region parked a worker and a connection for 20 s (deep-review round 5)."""
+    connection while it waits. It used to poll out the whole 20 s for a name that could never appear
+    — an ordinary seek past the produced region was enough to park a worker and a connection, and
+    forty hopeless names parked the API (deep-review round 5). ffmpeg writes segments in order, so a
+    segment whose predecessor is absent is not the next one, and that is knowable at once — even
+    while ffmpeg is still running, which is the case `proc` alone cannot shorten."""
     d = tmp_path / "m1_0_0_+0.00"
     d.mkdir()
-    sessions["m1"] = _Session("sid-a", d)  # its _Proc.poll() reports a finished ffmpeg
+    (d / "seg_0.ts").write_bytes(b"x")  # the session is producing; seg_99999 is simply not next
+    sessions["m1"] = _Session("sid-a", d, running=True)
     client = _client(db, monkeypatch)
     started = time.monotonic()
     try: