I cannot reproduce this issue using [bd] API on my test board. In your error, it is complaining that ./vault/config.php cannot be opened. Either it is missing or does not have proper file permissions. Possibly you have the API on a sub-domain that is a clone of your domain directory, but you neglected to clone the /vault sub-directory.
Additionally, your site URL as specified in the Members Area does not appear to be valid, so I cannot run any tests because I do not know what your website is. Note that if your license is used on a site other than what is specified in the Members Area, license privileges may be revoked.