if its only a few GB or whatever, and not grossly complex, pg_dumpall -h oldhost | psql -h newhost, is the simplest way to move a complete set of databases from an old server to a new. if there are large tables with millions of rows indexed, make sure you set maintenance_work_mem on the new server to 2GB before running this.
it's a full copy from the production, so it's 2.3TB
Thats quite huge. pg_upgrade would be a better choice and yes, downtime is needed. You need to have the database shutdown all through the upgrade process.
How long it will take depends on type of Disks you have. It is definitely a lot faster than pg_dump/pg_restore.