How to manage pgsodium_root.key in primary-secondary cluster

[nemdo]

I have a primary-secondary cluster with automatic failover and load balancing. All nodes should have the same root key in pgsodium_root.key otherwise it will create conflicts on the secondary nodes, right?

If yes, should I replace/mount pgsodium_root.key after installation on the secondary nodes and everything will work correctly? There won't be any problems with the generated keys from the root key as those will be replicated on the secondary nodes?