The HTTP 403 is a HTTP status code meaning access to the requested resource is forbidden. The HTTP 404 means the requested resource could not be found.
For both cases, our guess is that the redirection to your website is blocked by your firewall plugin after the authentication.
You can verify this by temporarily deactivating the firewall plugin and try to connect to the storage again.
If that is the case, we would suggest you to configure your firewall plugin settings to allow the redirection to your website, or temporarily deactivate it before authenticating remote storage.
Additionally, if you have changed WordPress login URL by using a plugin, temporarily deactivate the plugin first, then try it again.