Unfortunately that's a manual change - as per https://video2.skills-academy.com/en-us/entra/identity/hybrid/connect/how-to-connect-sync-staging-server#staging-mode
A server in staging mode continues to receive changes from Active Directory and Microsoft Entra ID and can quickly take over the responsibilities of another server in the event of a failure. If you make configuration changes to your primary server, it is your responsibility to make the same changes to the server in staging mode.
A server in staging mode continues to receive changes from Active Directory and Microsoft Entra ID and can quickly take over the responsibilities of another server in the event of a failure. If you make configuration changes to your primary server, it is your responsibility to make the same changes to the server in staging mode.