feat: introduce custom provider example and remove redundant debug logs

- Added `examples/custom-provider/main.go` showcasing custom executor and translator integration using the SDK.
- Removed redundant debug logs from translator modules to enhance code cleanliness.
- Updated SDK documentation with new usage and advanced examples.
- Expanded the management API with new endpoints, including request logging and GPT-5 Codex features.

internal/translator/gemini/gemini/gemini_gemini_request.go

@@ -18,7 +18,6 @@ import (
 //
 // It keeps the payload otherwise unchanged.
 func ConvertGeminiRequestToGemini(_ string, inputRawJSON []byte, _ bool) []byte {
-	log.Debug("ConvertClaudeRequestToGemini")
 	rawJSON := bytes.Clone(inputRawJSON)
 	// Fast path: if no contents field, return as-is
 	contents := gjson.GetBytes(rawJSON, "contents")