[log] Add debug logging to server/handlers.go

[github-actions]

Summary

Added debug logging to internal/server/handlers.go to improve troubleshooting and development visibility.

Changes

Logger Declaration

• Added logHandlers debug logger with namespace server:handlers following the project's pkg:filename convention

Logging Enhancements (7 new statements)

1. OAuth Discovery Handler

   • Log handler creation
   • Log incoming OAuth discovery requests with remote address, method, and path

2. Close Endpoint Handler

   • Log handler creation
   • Log incoming close requests with remote address, method, and path
   • Log method validation failures
   • Log shutdown state checks (already closed scenario)
   • Log shutdown initiation
   • Log shutdown completion with server count

Benefits

• Troubleshooting: Debug logs provide context for request handling and shutdown sequences
• Zero Overhead: Logs only computed when DEBUG=server:handlers is set
• Dual Output: Logs written to both stderr (colored, with time diffs) and file logger (text-only)
• No Side Effects: All logger arguments are simple values, no function calls or computations

Testing

The changes follow the established logging patterns in the codebase and maintain consistency with other handlers.

Compliance

✅ Exactly 1 file modified (focused, single-file PR)
✅ No test files modified
✅ Logger naming follows pkg:filename convention
✅ Logger arguments have no side effects
✅ Logging messages are meaningful and helpful
✅ No duplicate logging with existing logs
✅ Follows AGENTS.md guidelines

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