There are a variety of high availability setup options for databases such as RDB high availability setup, RDB Replication setup, and LDAP Replication setup.
How does Identity Manager handle these types of databases being used as the object store for an environment?
IDM doesn't directly handle the replication or high availability of an object store database.
The database should be set up for high availability and replication on its own and IDM will connect with a JDBC datasource. The database layer will present a connection string to IDM. The presented connection string will be same as a string from a single database point of connection. If behind this connection there is HA db setup, cluster or replication it is hidden from IDM.