The logging level in the UniFi Controller doesn't seem to affect the logging level on the USG at least (more testing needed for APs). This will work for DHCPd and maybe DNSMasq, but haven't tested it yet.
The only catch [for now], is you have to use config.gateway.json (this file is on/needs to be created on the controller in the applicable site) to accomplish this (as of Controller 5.9.4).
If you need further information please see UniFi Advanced USG Configuration for help about where to create the config.gateway.json.
PLEASE NOTE:
Below is an example of the config.gateway.json needed to change logging for notice to info.
Note: All logging is in /var/log/messages
{ "system": { "syslog": { "global": { "facility": { "all": { "level": "info" } } } } } }