The web server doesn’t load up every file, there are handlers for different components, images, CSS files, javascript files as well as index.html and login.html, since there isn’t many html files and their needs are slightly different we handle them explicitly.
Is there a specific file at a specific URL that letsencypt is expecting?
At the moment there isn’t anything you can do to get the file served through Sonarr’s web server, you’d need to use another webserver to do that.
Supporting Let’s Encrypt is something we’ve discussed briefly, but its not something we’ve committed to supporting and with the current mono SSL implementation lacking support for modern protocols its not something we’re focusing on.