[Trace] Add timestamp logging to prover module for better traceability

[tuyndoan]

Dear Team,

I would like to propose adding timestamp logging to prover.rs as an initial step to improve log traceability and debugging capabilities. This change adds timestamps to proof generation logs while maintaining the current log format and structure.

The enhancement aims to provide better visibility into proof timing and execution flow, making it easier to:

• Track proof generation progress with precise timestamps
• Debug timing-related issues with orchestrator updates
• Analyze performance patterns across proof cycles
• Correlate events across different system components

The implementation is minimally invasive, only adding timestamps while preserving all existing log formatting and behavior.

Changes

• Added chrono::Local for timestamp generation in prover module
• Introduced println_with_time helper function and println_time! macro for prover logs
• Updated existing println statements in prover.rs to include timestamps
• Maintained all existing log formatting (colors, indentation, symbols)

Example log output:

[2024-12-13 14:30:45.123] ✓ Proved step 0 at 16.81 proof cycles/sec.
[2024-12-13 14:30:45.234] Will try sending update to orchestrator...

Notes

• No changes to existing functionality, purely logging enhancement
• Currently only applied to prover module, can extend to other modules if needed
• Minimal code changes, focusing only on log output format
• Zero impact on proof generation or verification logic

Thanks