carl I can't speak really for the rest of it, but I'm pretty sure the frames you see on hover are from a YouTube API, I don't believe Kagi is generating those themselves. In that case, considering actions YouTube's been taking recently (blocking VPNs, requiring login, blocking Invidious), getting video streams at scale might not be so trivial unfortunately.
I'm going off this StackOverflow post, which has some interesting info about the frames in question. Maybe some of the techniques you brought up could be applied with the storyboard images? Not as good as the full video but I'd imagine immensely cheaper.