Hello Soumyadeep,
The problem indeed exists, but IMO the "log" directory case must be handled differently:
1. We don't need or I would even say we don't want to sync log files from the new primary, because it destroys the actual logs, which could be very important to figure out what has happened with the old primary
2. Unlike "pg_wal", the "log" directory is not necessarily located inside PGDATA. The actual value is configured using "log_directory" GUC, which just happened to be "log" by default. And in fact actual values on source and target could be different.
Regards,
--
Alexander Kukushkin