Maybe you can use an informative log_line_prefix configuration, like
the proposed pg_badger one:
'%t [%p]: [%l-1] user=%u,db=%d,app=%a,client=%h '
This should give you more information about the real importance of the
error message to your use case. A FATAL error from user "postgres" or
"[unknown]" can be potentially more problematic than an error from
"user1". Also, postmaster messages won't have any of these variables
set:
2019-03-21 12:21:32 -03 [1714]: [17-1] user=,db=,app=,client= LOG:
checkpoint starting: time
--
----------
“Life beats down and crushes the soul and art reminds you that you have one.”
- Stella Adler