feat: Centralize logging setup with structlog integration

[khvn26]

Closes #31

Logging setup moves from Django settings into flagsmith-common, running before Django loads. Both stdlib and structlog now route through a single ProcessorFormatter, so all output (app code, structlog, Gunicorn error logs) shares the same format and ISO timestamps.

Key additions

• setup_logging() in common.core.logging — configures stdlib via dictConfig, then wires structlog through stdlib using LoggerFactory (not PrintLoggerFactory). Accepts application_loggers for per-package level control.
• build_processor_formatter() — shared formatter builder used by both the root logger and GunicornJsonCapableLogger, ensuring consistent rendering.
• sentry_processor in common.core.sentry — structlog processor that sets Sentry context from event dicts. Hardwired into the structlog processor chain. Since structlog routes through stdlib, Sentry's LoggingIntegration automatically captures ERROR+ logs.
• application_loggers allowlist — root logger stays at WARNING to suppress third-party noise; listed app loggers get the requested level. DEBUG overrides everything. Configurable via APPLICATION_LOGGERS env var (comma-separated).
• Gunicorn error logs now use ProcessorFormatter for both json and generic formats (access logs unchanged — still CLF for generic, GunicornAccessLogJsonFormatter for JSON).
• sentry-sdk added as an explicit dependency in the common-core group.

What it doesn't change

• JsonFormatter and JsonRecord stay for Gunicorn access log use.
• Gunicorn access log format (CLF) is untouched.

Migration guide for flagsmith/flagsmith

1. Replace the LOGGING dict in settings/common.py

# Remove the entire LOGGING = { ... } block (lines ~615-668) and replace with:
LOGGING = {"version": 1, "disable_existing_loggers": False}

Django's dictConfig(LOGGING) call during django.setup() becomes a no-op.

2. Set APPLICATION_LOGGERS env var

APPLICATION_LOGGERS=app,features,integrations,task_processor,app_analytics,webhooks

This ensures app loggers are at the correct level from boot.

3. Delete api/util/logging.py

It duplicates JsonFormatter which now lives in common.core.logging.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.36%. Comparing base (398c83c) to head (ca49486).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #179      +/-   ##
==========================================
+ Coverage   96.12%   96.36%   +0.24%     
==========================================
  Files          92       96       +4     
  Lines        3222     3441     +219     
==========================================
+ Hits         3097     3316     +219     
  Misses        125      125              

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