Add structured logging with contextual information

[sfloess]

Part of #27: Improve Error Handling and Logging

Scope

Enhance logging to include structured contextual information (provider name, request ID, model, timing) to make log output useful for debugging.

What to do

• Add provider name and model to all AI-related log messages
• Log request/response timing for performance monitoring
• Log request IDs returned by AI APIs for support correlation
• Use parameterized log messages: logger.log(Level.INFO, "Request to {0} completed in {1}ms", new Object[]{provider, elapsed})
• Add Level.FINE logging for request/response payloads (for debug mode, not production)

Acceptance criteria

• All AI-related log messages include provider name
• API call durations are logged at INFO level
• Debug-level logging available for request/response payloads
• Log messages use parameterized format (not string concatenation)