Migrate Existing Code to Pino Logger

[otobot1]

Is your feature request related to a problem? Please describe.
The pino logger has been implemented, but all of the code written previously doesn't use it.

Describe the solution you'd like
Update the CelesteMods source code to use the pino logger. Replace all console.log instances with calls to the pino logger. Add appropriate info logging, primarily to our API (mod created, user login, map changed, etc). Add/remove logging as needed/appropriate for consistency. Other changes as required.

Describe alternatives you've considered
N/A. This is required eventually.

Additional context
Follow-up to #548. Some of this work can be done at any time, but #554 will need to be completed before this issue can be fully resolved.