Captioning mismatch when videos have no dialogue

What happens is when the video has a long silent period (like an intro) the captions start playing but the actual dialogue starts later. For about ~30-40s the captions are correct and ahead but at some point it does correct itself. For example in STAT 420 lecture `uuid=5cf8d03c-88bb-4e32-95fb-075c90265bf4` where the speaking starts at around 8 seconds but the captions start playing earlier.


I think I've also seen it in the middle of videos where there is a silence and the rest of the captioning gets an offset from then on as well.

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I'm not sure if this has been brought up before, but I on quick glance of the issues on `FrontEnd` and `WebAPI` I couldn't find an issue related to this. I've reported to professors I've had issues with synchronization but I'm not sure where that ended up. I've noticed this in several courses over the year (CS 241, 357, 418, STAT 420) and was one of the main reasons I didn't use classtranscribe for the longest time.

Start by reproducing the mismatch with the STAT 420 video UUID 5cf8d03c-88bb-4e32-95fb-075c90265bf4, especially the silent period before speech begins. Trace how the FrontEnd starts and maintains caption playback during silence, then compare behavior across the reported courses. Done means captions remain synchronized through initial and mid-video silent periods.

Written by the indexing model from the issue text.