Which solution will meet these requirements with the LEAST operational overhead?

Explanations:

Creating a DB snapshot of the RDS for PostgreSQL instance will lead to downtime during the snapshot process, and the snapshot will not capture ongoing changes while the snapshot is being created. This method does not minimize downtime or data loss effectively.

Creating an Aurora read replica of the RDS for PostgreSQL instance allows for near real-time replication with minimal downtime. Once the replication is set up, the Aurora read replica can be promoted to a standalone Aurora DB cluster, allowing for a seamless transition with little to no data loss. This approach involves the least operational overhead.

Using data import from Amazon S3 to migrate the database to Aurora PostgreSQL is not ideal for minimizing downtime, as it would involve exporting data, potentially leading to significant downtime and data loss. This method is operationally heavier and slower compared to using read replicas.

The pg_dump utility can be used to back up the RDS for PostgreSQL database, but restoring from this backup to a new Aurora PostgreSQL cluster would also lead to considerable downtime while the data is being exported and imported. This option is more complex and operationally intensive than using a read replica.