The streaming replica's are indeed in read only mode. Any cluster operations you will want to perform are needed to be performed on the primary coordinator.
What is it that you try to accomplish by adding workers to the replica coordinator?
The replica coordinator should have the primary worker nodes in pg_dist_node.
After a failover of the coordinator the worker nodes are not necessarily failing over, meaning, the failed over coordinator would need to talk not to the secondary workers that you just setup. Instead they will connect to the nodes that were the last known working primary workers.
If, during a failover, you actually fail over both the coordinators and the workers you will want to update the node information on the coordinator right after the failover. As always, these operations need to be performed on the coordinator that is the primary in your setup.
However, if only 1 of the worker nodes fails over you update this on the primary worker. This change gets streamed to the standby coordinator from there.
-- Nils