Are you flash constrained or RAM-constrained?
Log messages are only stored in flash (in the application binary), not in RAM, and all nRF52 and STM32 devices use XIP to execute directly from flash, including static data and string contants.
If you are flash constrained, first try removing the SerialLogHandler. This should reduce some of the usage, even if you leave the Log.info calls in.
And of course the messages generated by the system will have no effect on your application binary size.