Before going with the full service + postgres implementation in EB for metabase, it’s worth noting that using the RDS instance deployed by EB is not recommended for production environments.
The recommendation is to deploy a non-EB RDS PG instance, and then use EB for just the MB service.
See this thread for more info: Best practice for having RDS as part of EB environment and follow the link to AWS for a guide on how to decouple the service from the persistence.