[OrderlyTiamat]

this is not a complete solution, but you seem to know what videos you're going to search through rather than wanting to search through everything. If that's the case, I recommend downloading the subtitles for every video via yt-dlp [1] as shown in this stackoverflow question [2] (it doesn't download the video itself this way to save bandwidth):

    yt-dlp --all-subs --skip-download https://www.youtube.com/watch?v=Ye8mB6VsUHw

(The answer uses youtube-dl, but I prefer yt-dlp, it works with these same options when I tried it)

When you've downloaded all subtitles, you can simply grep through them. I hope this helps!

[1] https://github.com/yt-dlp/yt-dlp

[2] https://superuser.com/a/927532/1071647