After searching for such a thing for a long time, I've just discovered that yt-dlp, which I already have installed and use daily to download YouTube (and other) videos, supports fetching the user comments and saving them as a JSON file.
But, frustratingly, I cannot find any option to only do that, and not also download the video at the same time. How is that done? Is it even possible? If not, that's such a shame, since this is an amazing "stand-alone" feature which I often want to do without having to also download the massive video file. It's near-impossible to implement myself because YouTube makes it extremely difficult and convoluted to stop bots/automation.
I've looked at this manual for a long time now: https://github.com/yt-dlp/yt-dlp