Standardize server logging and lifecycle diagnostics

[ViTeXFTW]

Summary

• Standardize user-facing lifecycle messages through window/logMessage and developer diagnostics through structured tracing logs.
• Keep stdout protocol-only, add indexing and document refresh telemetry, and document logging conventions.
• Update server logging coverage, configuration handling, and end-to-end expectations.

Tests

• Ran the relevant Rust and end-to-end server tests.

Checklist

• I kept the change focused.
• I ran the relevant checks or explained why they were skipped.
• I did not commit generated artifacts, game source, corpus data, or secrets.