Basically, you spin up a new Blue Green deployment with any desired changes (in our case, we were upgrading Postgres major from 13 to 15). While your blue configuration continues to serve traffic, AWS uses logical replication to keep the "green" deployment in-sync. You can keep modifying (or testing) the "green" deployment (eg you could load test it if you wanted to), as long as you don't do any writes to it (writes still have to go to your live, blue configuration, and are replicated to green).
When you're ready, you run the "switch" command, and AWS does a few things for you: run checks to ensure blue/green are in sync, stops writes and connections, waits a few seconds to ensure replication is caught up, renames your database, then allows connections/writes again. We had less than 20 seconds of downtime, by our count. And, we had a primary and several read replicas and AWS successfully switched the full configuration over with no hiccups. You don't even need to switch your configuration because AWS swaps the database URLs for you. Green becomes blue, blue becomes old blue, and when you're ready, you delete "old blue".
Highly recommend! They do have some restrictions (for instance, not sure if it would work if you're switching accounts, etc).
1. https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/blue-...