Fix logging config for the docker image (#6197)

Turns out that loggers that are instantiated before the config is loaded get
turned off.

Also bring the logging config that is generated by --generate-config into line.

Fixes #6194.

changelog.d/6197.docker

@@ -0,0 +1 @@
+Fix logging getting lost for the docker image.

docker/conf/log.config

@@ -24,3 +24,5 @@ loggers:
 root:
     level: {{ SYNAPSE_LOG_LEVEL or "INFO" }}
     handlers: [console]
+
+disable_existing_loggers: false

synapse/config/logger.py

@@ -68,9 +68,6 @@ handlers:
         filters: [context]
 
 loggers:
-    synapse:
-        level: INFO
-
     synapse.storage.SQL:
         # beware: increasing this to DEBUG will make synapse log sensitive
         # information such as access tokens.
@@ -79,6 +76,8 @@ loggers:
 root:
     level: INFO
     handlers: [file, console]
+
+disable_existing_loggers: false
 """
 )