Problem solved. SQL Server didn't accept the authentification. We changed from Windows Authentification only to SQL User and Windows Authentification.
That disturbed the connection between veeam one and SQL Server. A Restart of the sql service solved the problem.
Maybe it's an idea to generate an additional error to inform the user/admin that the sql connection has errors.
The Description of the VeeamBpPerfCollectionFailedEvent let you focus on the Backup Server Infrastructure and not the sql