Shutdown mode fast for stopping PostgresSQL standby server
A WAL receiver is neither an active client, nor an online backup. So a so-called "smart" shutdown executed on the master will not wait indefinitely for the WAL receiver to go away on its own.  Rather, it will actively disconnect the WAL receiver.  This is pretty much the last thing it does--it waits for the shutdown checkpoint to finish, and streams the WAL containing that checkpoint record over to the replica, and then disconnects it.

If you are concerned about "If the server is in hot standby, recovery and streaming replication will be terminated once all clients have disconnected", that is describing what happens when smart shutdown is initiated against the replica, not against the master.  The master is never "in hot standby", that is a status that only a replica can be in.