feat(caption): stream live captions and polish finished lines in context

Replaces the fixed six-second batches with a streaming track per audio
source: the uncommitted audio is re-recognised every second and sent as a
partial with its agreed (stable) prefix, a short pause finalises the line,
and long unbroken speech is committed at Whisper segment boundaries. Idle
audio is trimmed so silence cannot produce invented sentences.

Finished lines are corrected by the local model against the previous lines
and replaced in place; edits that change too much are rejected. The
behaviour can be switched off in Settings.

packages/i18n/src/locales/ko.json

@@ -1910,5 +1910,7 @@
   "input.feedback.excludedFailed": "제외 목록을 저장하지 못했습니다.",
   "input.feedback.recommendationFailed": "{{app}}을(를) 제외 목록에 추가하지 못했습니다.",
   "popup.caption.waiting": "듣는 중… 첫 자막까지 몇 초 걸릴 수 있어요",
-  "popup.caption.dragHint": "끌어서 이동 · 더블클릭하면 원위치"
+  "popup.caption.dragHint": "끌어서 이동 · 더블클릭하면 원위치",
+  "settings.captionRefine": "자막 문맥 다듬기",
+  "settings.captionRefine.desc": "확정된 자막을 로컬 AI가 앞뒤 문맥에 맞게 띄어쓰기·문장부호·잘못 들은 단어를 고칩니다."
 }