Kobo Sync as it's called in the documentation (https://github.com/janeczku/calibre-web/wiki/Kobo-Integratio...) works very well, and is very easily enabled (updating a single line in a config file on the ereader that appears when you mount it on your computer).
It will convert books to Kepub automatically and you can select to only sync certain shelfs.
It will convert books to Kepub automatically and you can select to only sync certain shelfs.