Good news - at least for rclone:) This is what I suspected from the beginning but it is not easy to prove.
Real time or at least close to real time would be only possible if remote had capability to inform rclone that something changed, e.g. something like watch path for local macOS filesystem . Webdav (and most cloud storages) has no such functionality so it is impossible.
Now how rclone deal with it? VFS directory cache is valid only for specific amount of time - when this time passes trying to read given directory will result with rclone checking changes on remote instead of relying on cache. It is controlled by flags:
--dir-cache-time duration Time to cache directory entries for (default 5m0s)
--poll-interval duration Time to wait between polling for changes. Must be smaller than dir-cache-time. Only on supported remotes. Set to 0 to disable (default 1m0s)
Webdav is not polling remote so you are only left with --dir-cache-time duration. You can set it to 1s but then effectively you do not use directory cache. Myself I set it to 15min - I am not in a such hurry to be "real time" up to date. You have to decide yourself what is the best for your workload.
PS. If you are using FUSE-T check this link - macOS rclone mount - new FUSE-T released - old issues fixed