fix: harden AI subtitle fix response parsing

changes/task-117.1.md

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+type: fixed
+area: launcher
+
+- Hardened YouTube AI subtitle fixing so fenced SRT output and text-only one-cue-per-block responses can still be applied without losing original cue timing.

changes/task-130.md

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+type: fixed
+area: launcher
+
+- Keep the background SubMiner process running after a launcher-managed mpv session exits so the next mpv instance can reconnect without restarting the app.
+- Reuse prior tokenization readiness after the background app is already warm so reopening a video does not pause again waiting for duplicate warmup completion.