Use Azure Database Migration Service to perform a managed migration of the on premise PostgreSQL database is the correct option.

Azure Database Migration Service provides a guided and managed migration path for PostgreSQL migrations to Azure Database for PostgreSQL and it supports both offline and online migration scenarios which helps reduce downtime and automate schema and data movement. It integrates with Azure services and it handles validation and cutover tasks so large or production migrations are safer and less manual than ad hoc approaches.

Use Azure Data Factory to copy the data from the on premise PostgreSQL to the Azure database is not the recommended choice because Data Factory is an ETL and bulk data movement tool and it does not provide a full database migration workflow with schema conversion, validation, or orchestrated cutover. You could use it to copy tables but you would need extra manual steps to handle schema and to minimize downtime.

Export a logical SQL dump from the local PostgreSQL and then import that dump into the Azure Database for PostgreSQL instance is technically possible for small or simple databases but it is not ideal for production migrations because it is manual, often requires extended downtime, and does not provide automated validation or incremental synchronization for cutover.

Set up a site to site VPN and stream replication traffic directly into the Azure database is incorrect because managed Azure Database for PostgreSQL does not support acting as a physical streaming replica of an external primary. Streaming physical replication into the managed service from an on premise server is not supported and you would instead use supported logical replication or a managed migration tool for continuous or near zero downtime migrations.

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