feat(host-control-mode): localize the in-page dialog & badge

The host-control desync dialog and the "watching on your own" badge were
hardcoded English — content.js has no i18n loader. Background does, so it now
resolves the strings (GET_HCM_STRINGS: loadLocale + getMessage) and content
fetches them on init with English fallbacks, re-rendering the badge if it was
already shown. The dialog body is now generic (dropped the paused/jumped verb)
to keep translation clean across languages.

Adds 6 keys (HCM_DIALOG_TITLE/BODY/STAY/SOLO, HCM_BADGE_SOLO/RESYNC) translated
across all 15 popup locales.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

extension/locales/ko.json

@@ -52,6 +52,12 @@
   "BADGE_GUEST": "게스트",
   "BADGE_DESYNCED": "단독",
   "TOOLTIP_PEER_DESYNCED": "혼자 시청 중 — 호스트 명령을 무시합니다",
+  "HCM_DIALOG_TITLE": "KoalaSync · 호스트가 이 방을 제어합니다",
+  "HCM_DIALOG_BODY": "이 방에서는 호스트만 재생을 제어할 수 있습니다. 계속 함께 보시겠어요, 아니면 혼자 보시겠어요?",
+  "HCM_DIALOG_STAY": "동기화 유지",
+  "HCM_DIALOG_SOLO": "혼자 보기",
+  "HCM_BADGE_SOLO": "혼자 시청 중",
+  "HCM_BADGE_RESYNC": "다시 동기화",
   "NO_PEERS_CONNECTED": "연결된 참여자가 없습니다",
   "BTN_LEAVE_ROOM": "방 나가기",
   "LABEL_SELECT_VIDEO": "비디오 선택",