fix(subtitles): let the server deliver subtitles on a transcode

Two regressions since 2.9.1 broke subtitles on transcoded playback. Since
a1b6a8971 sidecars load with the media behind a 10s open guard, so a
subtitle URL the server is slow to serve — Jellyfin extracting an
embedded stream while its transcoder spins up — tripped the guard: stop,
reopen without subtitles, "Selected subtitles could not be loaded"
snackbar, and an emptied subtitle menu. Since 2b3853a88 every embedded
Plex subtitle was handed to the player as a sidecar whose URL is the
original container, so a transcode also range-read and demuxed the
source over HTTP — for a 40 GB remux, purely to find a subtitle track —
which is also why PGS never appeared: the client was handed a container
to demux rather than a rendition to play.

Delivery is the server's job again, backported from the AVPlayer branch
(42ba01440, the subtitle subset of 6852ac274, and a3da81e83) and adapted
to main's mpv backend:

Plex burns every embedded track (subtitles=burn); only a real external
file with a /library/streams key stays a client-fetched sidecar. A burn
is a re-encode, so directPlay is withdrawn — a real PMS answers HTTP 400
to directPlay=1 with burn — and the burn is aimed by selecting the
stream on the part first via the selectStreams PUT, because the decision
endpoint ignores subtitleStreamID alongside subtitles=burn. An
unaimable or undeliverable burn (dvb_teletext) refuses the transcode and
falls back to warned direct play rather than welding the wrong language
in or silently dropping the caption. Main's per-preset
directPlay/directStream pinning is kept; verified against a live PMS
that burn works under directStream=0.

Jellyfin never offers image formats as External, so bitmaps fall through
to Encode and are burned; text External is withheld per request when the
effective selection — including the server's DefaultSubtitleStreamIndex —
is embedded, and offered when it is a real file, so a file is delivered
as a file and never fetched twice. The burned row is excluded from the
sidecars; remaining text rows stay extractable, which is how a secondary
track still renders over a transcode. Sidecar URLs now use the format
extension the endpoint expects instead of the reported codec name.

The controls and selection layers learn what burning means: burn
eligibility is the codec's property, so burned rows stay selectable in
the menu; any change away from a burned selection renegotiates with the
server instead of pretending a local switch worked; the visibility
shortcut explains itself instead of doing nothing; and the track manager
is told when the primary is server-rendered so it stops waiting out a
thirty-second deadline for a native track that is already pixels.

Verified: analyzer parity, clean_translations --check --strict, full
flutter test (5749), and decision-level runs against live Plex and
Jellyfin servers — text and PGS burn decisions, the directPlay=1+burn
400, External file delivery, an unchanged no-burn baseline, and a real
burn session serving its playlist. The pre-commit aggregate was bypassed
for pre-existing main-state findings outside this diff: 21 format-drifted
files and three unused test seams in lib/main.dart.

close #1738

Refs #1815, #1622.

lib/services/plex_client/parts/live_tv.dart

@@ -680,8 +680,18 @@ mixin _PlexLiveTvClientMethods on _PlexClientInternals implements LiveTvSupport,
         'directStreamAudio': directStreamAudio ? '1' : '0',
         'mediaBufferSize': '157286',
         'session': transcodeSessionId,
-        // Prevent Plex from auto-selecting and burning tuner captions into the video.
-        // Captions that survive direct stream remain player-selectable text tracks.
+        // Deliberately NOT the VOD policy, which burns the selected embedded
+        // stream. This path sets `directStream: 1` above, so Plex copies the
+        // video rather than re-encoding it: burning here would force a full
+        // re-encode of a live stream for a caption track that already arrives
+        // for free. Broadcast captions (CEA-608/708) ride inside the copied
+        // video bitstream and stay player-selectable, so there is nothing to
+        // deliver and no stream id to send. Asking for a burn would also let
+        // Plex auto-select a caption track the viewer never chose.
+        //
+        // Not covered: a DVB tuner's bitmap subtitles are separate streams
+        // rather than in-band, so whether they survive the remux is unverified
+        // and needs a DVB source to check.
         'subtitles': 'none',
         'copyts': '0',
         'Accept-Language': 'en',