There are a lot of gotchas with using DMS (which seems to use pglogical under the hood). Since it’s not hardware-level replication, you can run into issues with large rows/columns/tables and it doesn’t really handle foreign keys. It may not handle some special data types at all. You also need to update the sequences after the migration or you’ll get errors about duplicate primary keys. You can also have issues if you don’t have proper primary keys, because it doesn’t always copy the entire row at once.

If the databases are within the same AWS account, it’s likely easier to use hardware-level replication with global database or snapshots to do migrations if you’re ok with 4-5 mins of downtime.