Hi,
This ensures that the LSN numbering is consistent between master and replica. And yes if you want automated failover then you'd need to rely on haproxy or you'd ned to manually update/switch hostname.
Unfortunately I cannot say anything about Patroni. But if Patroni can guarantee LSN numbering to be consistent then it is safe to use it too.
WRT slot.failover - this is used in createion of the slot only so if the slot already exists then the setting is not used at all.
Jiri