How do you make a managed relational database highly available?

Run it multi availability zone, so there is a synchronous standby in another zone and failover is automatic, typically within a minute or two. Read replicas are for read scaling, not availability, because replication is asynchronous and can lag. Back that with automated backups and point in time recovery, connect through the cluster endpoint or a proxy so failover is handled, and actually test failover rather than trusting it.

Multi availability zone is the core of it: a synchronous standby in a second zone, and the managed service promotes it if the primary fails, usually inside a minute or two. The distinction I always make explicit is that a read replica is not a failover target, it is asynchronous, so promoting one can mean losing recent writes; it is there for read scale. Durability is separate again, so automated backups plus point in time recovery, and I copy those into another region because a highly available database that only exists in one region is still one bad day away from gone. The part people forget is the application. Failover changes which host the endpoint points at, so a connection pool holding stale connections or a runtime caching DNS forever will keep failing after the database is healthy again. So I connect through the cluster endpoint or a proxy, set sensible pool validation, and make sure retries are safe. And I test it, by triggering a failover in a lower environment and timing how long the application takes to recover, because that number is always worse than the advertised one.