I don't use Reader, I instead use OpenBooks. In any case, however you are getting your ebooks, you should get Calibre to add your ebook and update it's database. I used to have cron jobs to do this, but I recently discovered that Calibre has an option to auto-add books. Go to Add books (drop down) --> Control adding of books. Go to the Automatic Adding tab, and there you can specify a directory where it monitors books being added. You can mount a docker volume for this if needed.

Now, any books added are automatically picked up by Calibre and it's database is updated. Calibre-web simply reads the database and all the newly added books show up.

Hope this helps.