In your original post you mentioned that you “uninstalled the standard zwave-js from the integrations”. If you truly meant “integration” and not “add-on”, then that uninstall would remove all of the Z-Wave devices and entities. Adding the integration will bring them back.
Usually the “Failed to Connect” error would mean the add-on is not running properly. Also double check that you didn’t add any extra trailing whitespace for the URL, e.g. "ws://a0d7b954-zwavejs2mqtt:3000 " (which can happen with copy/paste), the dialog will not clean those out and it will fail to connect.
You could try looking at this guide, which provides more detail than the docs. If ZUI is already running successfully you can skip the parts about restoring the cache, or any other details that don’t apply.
If all that fails, feel free to post the driver debug logs from ZUI, to see if there’s some other issue. If you have a 500-series controller (Aeotec Gen5, etc.) be sure to disable Soft Reset in the Z-Wave settings.