Use a custom logging library

[moltony]

While Python's built-in logging module is convenient, I want to write a new logging system specifically for Backup-chan. It would have an interface similar to the logging module, but would also have some custom features:

• Logging as JSON files or whatever other easily parsable format. This allows me to show logs in a pretty way without doing log file splits and stuff.
• Archiving old log files. They can be compressed and sit on the disk.
• Backup-chan-specific fields, such as what target or backup processing task caused the message.