[Feature] Logging to file.

[lastrosade]

Feature Summary

The strangely missing log to file feature.

Detailed Description

I can't believe it took me this long to realize there's no log to file CLI argument.
I am currently trying to test perf on various models and settings.
Using tee leads to the dreaded stairs of doom:

Stairs

We even get broken unicode for free!

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I think it would be beneficiary to include a log to file argument similar to what llama.cpp has, especially now that this project has a functional (WIP but still) server.

These are the flags I am thinking about:

--log-file FNAME                        Log to file
--log-prefix                            Enable prefix in log messages
--log-timestamps                        Enable timestamps in log messages
--log-verbosity N   Set the verbosity threshold. Messages with a higher verbosity will be
                    ignored. Values:
                     - 0: generic output
                     - 1: error
                     - 2: warning
                     - 3: info
                     - 4: debug
                    (default: 1)

If possible, have a separate --verbosity N or --stdout-verbosity N that controls stdout output. So tmux/whatever you use stays clean while the log file fills up.

Alternatives you considered

tee and suffering
powershell + tee + duckdb lmao (I won't share, I am ashamed)

Additional context

inb4 you can do that with env vars, but it's undocumented.