feat: adopt pino for structured JSON logging

[drifterza]

Closes #279

Description

Switches our internal logger implementation from a custom one-off module to use Pino for structured JSON observability, which allows for easier integration with ingestion endpoints like Datadog or ELK.

Acceptance Criteria

• Standardizes logging context through a heavily robust, highly performant structured logger
• Correctly segregates level payloads (info, warn, error, debug) with associated log metadata (e.g., categories)
• Retains backwards compatibility with HEADPLANE_DEBUG_LOG directives to suppress verbose logging when disabled locally without throwing errors
• Extends the Vitest mock ecosystem using standard stdout interceptors to adequately snapshot outputs natively