find error log for streaming replication

Recently the streaming replication fails after I restart the primary. I can not find the record using select * from pg_stat_replication Now, I want to see it from the system log file at /var/log/postgresql# on the primary. I find the following using grep -i -m 10 **fatal** postgresql-12-main.log: 2022-12-06 01:56:01.890 UTC FATAL: remaining connection slots are reserved for non-replication superuser connections 2022-12-05 11:36:57.024 UTC LOG: background worker "logical replication launcher" (PID 27089) exited with exit code 1 2022-12-05 11:36:57.637 UTC rep_user@[unknown] LOG: standby "12/main" is now a synchronous standby with priority 1 2022-12-06 01:55:27.344 UTC FATAL: remaining connection slots are reserved for non-replication superuser connections I have tried some keywords that might be able to be grep-ed like : replication, slave, ip address of the client and physical. But I do not find anything. BTW, I do not turn on the postgres log file so there is no file at var/lib/postgresql/12/main/log. There is no error on the replica side. I have grep keyword like fatal and error. Nothing. What are the keywords that I can grep to find errors related to replication? thanks