That's a great use case for LLMs, actually. Translate the sentence only up to what has been said so far. Basically, a balance between translating word-for-word (perfect timing, but terrible grammar) and translating the whole sentence and/or thought (perfect grammar and meaning, but potentially terrible timing).

With the SRT file format for subtitles, I think, there's no reason why one couldn't make groups of words appear as they are spoken.

Actually, I have to do the same thing when generating the dubbed voices. Otherwise it feels as though the AI voice is saying something different than the person in the video, especially when the AI finishes speaking and you still hear some of the last words from the original speaker.