You may google out several explanations on an error "WebSocket network error: The operation couldn't be completed (OSStatus error -9829)" when you attempt to connect to a secure websocket using Safari web-browser on Mac OS X 11.0.1 (Big Sur). One of them points out more strict requirements for trusted web-site certificates on MacOS an iOS, which I didn't know.
However, in my case the error was caused by a drawback in Safari browser, - turn out it simply does not send user certificate when performing secure websocket connection (wss:// URL scheme).
Hopefully, Firefox browser doesn't have this drawback and all works fine when you use it. Though you would need to install all CA certificates and user certificate into Firefox's store as it turn out doesn't use the system's one.