Clean up logging system (part 1 of 2).

* Rename LogManager::Log to LogManager::Write which is less repetitive.
* Accept a LogLevel instead of an int in logging methods
* Purge a ton of code related to non <log> related logging.
* Move LogHeader to LogStream.
* Move LogLevel enum from filelogger to logger.

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The second part of this will be slightly more tweaky. I'm filing this part now to avoid a ton of merge conflicts later.