http://bentasker.i2p/posts/blog/general/containerising-and-deploying-calibres-content-server-to-allow-web-annotations.html
It turned out that there's a Calibre integration plugin for Obsidian, which communicates with the Content Server. So, as well as being able to read books in a web browser, I can also use Obsidian: All of the underlying functionality (annotations etc) works. That's not too surprising as, after all, Obsidian's an electron app and so is really just a glorified web browser.