Hi PL,
SQL instance should be in the unlocked state for the DBs to be available for backups.
As you mentioned earlier the 'red lock' shows that your SQL instance is in a locked state. This is indeed a permission issue.
For SQL authentication on Windows hosts, set up a Run As credential for a user with SQL Server sysadmin permissions. The SQL authentication method authenticates against a SQL Server instance. This means that a SQL Server instance must be discovered in SnapCenter. You need SQL Server authentication for performing operations such as scheduling or discovering resources.
When you are creating a RunAs, you can select the SQL Server authentication mode.
You can also choose Windows authentication if the Windows user (with administrative privileges) that you are specifying has sysadmin rights/privileges on the SQL server.