Veeam Support gave me a call half an hour after the appointment and gave the User for "Veeam Backup Service" sysadmin rights on the SQL Server instance. He did not even asked me if he could give the user sysadmin rights.
I asked the Support if this is neccessary and explained that SQL sysadmin rights were not neccessary since Veeam v6, and that the user just has db_owner permissions on the db.
He told me that it is neccessary that this user has sysadmin rights on the sql instance and did not explain anything further.
The service then started fine.
I removed the sysadmin rights again because it does not comply with our regulations, and restarted the Veeam Server and the service is running. Maybe after Upgrade 2 some operations needed to take place and more permissions were neccessary for a short time. Not concinved from Veeam Support.
According this sysadmin rights are not neccessary: https://helpcenter.veeam.com/backup/vsp ... sions.html
Microsoft SQL Server
The account used to run Veeam Backup Service requires db_datareader and db_datawriter roles as well as permissions to execute stored procedures for the configuration database on the Microsoft SQL Server. Alternatively, you can assign db_owner role for this database to the service account.