SharDB isn't tailored for implementing a different DB for each site. However, if you don't have a large number of sites, you can use the VIP DB configuration to use a separate DB for each site.
Does the user root have permission to use the wp_home database?
By virtue of being the super user, root typically has access to all databases. Unless it's a local development install, using the root user in your wp-config.php should be avoided.
On some systems the name of your database is prefixed with your username
The main place I have seen that is cPanel implementations. If you used cPanel to create your databases then your
- shardb_prefix would be something like account_dbname_
- DBs would be named account_dbname_global, account_dbname_0, account_dbname_1, etc.
You can edit your wp-config.php to see the user that WP is using for the databases. If your DBs follow the naming convention I've outlined then check that the user has access to those databases.