Right now the best you can do is a scheduled cutover. This isn't as bad as it sounds because you can provision the new instance, import the production data and test everything before final sync and cutover.
As someone who has done this multiple times in the past I have to disagree.
Yes, it is very much as bad as it sounds and a big pain point with Postgresql in general and RDS in particular.
For small databases it may be considered a mere nuisance. But when your pg_dump takes an hour to complete then the whole "final sync and cutover" becomes a real problem.
this is pretty much a problem with RDS only. Postgres itself offers pg_upgrade which can do even huge databases (2 TB here) in seconds.
That depends on various factors. Sometimes pg_upgrade has to copy all your data. In those cases and for 2T you'll be measuring the wait in hours, not seconds.
https://aws.amazon.com/blogs/aws/rds-postgres-read-replicas/