I've sent you a direct message about this.
For the benefit of other users the first thing to check when debugging WebDAV issues is that the SSL/TLS certificate on the server is one supported by iOS. You can see a list of supported certificates here - https://support.apple.com/en-gb/HT209144. The other thing to then look at is for any debug shown when you type - including the parentheses
into the beorg REPL (go to Settings tab and then tap the button top right).
When trying to sync via WebDAV (to ownCloud server) I just get the message "Syncing org files..." at the top of the screen with a never-ending spinning ring. I trust my URL and credentials are correct as I successfully logged in to my ownCloud server with the WebDAV Nav app. Furthermore, when I intentionally mistype my login credentials the message and spinning ring go away after a few seconds.
I'm really excited to start using this app if I can get WebDAV syncing working.