Can I bind the widget to a specific thread instead of the current page URL?

Yes. Add data-key to the embed div:

<div class="bolmol-comments" data-key="my-blog/hello-world"></div>

The key is normalised the same way as a URL, then hashed to the thread identifier. Use this when the same content lives at multiple URLs, when the URL changes over time and you want the comments to follow the thread, or when you want to bind comments to something that is not a URL at all.