It’s sad that for this question (“What Python webdav library to use?”), which for sure interests more than one person, unrelated answer was accepted (“don’t use Python webdav library”). Well, common problem on Stackexchange.
For people who will be looking for real answers, and given the requirements in the original question (simple API similar to “os” module), I may suggest easywebdav, which has very easy API and even nice and simple implementation, offering upload/download and few file/dir management methods. Due to simple implementation, it so far doesn’t support directory listing, but bug for that was filed, and the author intends to add it.