On docs.rs i found only nxcloud, but this is not a library.
Searching for WebDAV returns a ton of hits, but which one should you pick for Nextcloud?
Depends what you want to do. If it is just to access files, a basic webdav library is probably a good choice and you can use one that is well maintained. Your list will be shortened if you just consider webdav clients and stuff that is actively maintained.
Specific Nextcloud libraries are useful if you want to use other API functions (e.g. create shares:
https://docs.nextcloud.com/server/latest/developer_manual/client_apis/index.html
or do stuff yourself if you don’t find it.
Perhaps there is someone here on the forum that works with Rust and Nextcloud.