Restore from remote server possible?

I have three machines, PROD, STAGE, BACKUP. BACKUP is docker container that runs pghoard. BACKUP uses a replica slot to backup PROD. Before a deployment I use pghoard_restore to setup STAGE with the most recent data from PROD (without any additional load on PROD).

I upgraded BACKUP last night now STAGE can't perform a restore. It seems like without a shared filesystem there isn't a way to get the xlogs that STAGE needs to make the base backup consistent from the the object store. The pghoard_postgres_command that is set in recovery.conf restores the necessary files to BACKUP (not STAGE where they are needed).

Could you provide some information about the vision of how recovery is supposed to work? Is my use case wildly different than what you imagined? Am I supposed modify the config so that I can safely run it locally on STAGE then interact with that instance of pghoard?