So, unfortunately, at the moment, we lack a straightforward method for transferring services or databases between accounts. You will need to recreate the services in the new account. As you mentioned, this process is relatively simple for non-database services or services without attached disks; you just replicate the configuration and select the same repository.
For databases, you will need to create a new database in the second account and then use pg_dump and pg_restore to migrate the data from the old database to the new one before deleting the old database.