Use logging instead of prints, enable timestamps

The logging subsystem is more versatile and provides more features than manual log prints. Timestamps are very often useful for tracking down timing issues, enable them for the root logger.

This current logging configuration doesn’t include the module/logger name in the message format as it clutters the logs. This may be revisited later when the logging system is overhauled to support structured logging and better tracing.

Quart/Hypercorn’s logger has its own log printing handler, so as we currently only print logs on the stdout, we need to disable the propagation to prevent access logs from being duplicated.