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/openai/chat-completions/gemini_openai_request.go

@@ -25,7 +25,6 @@ import (
 // Returns:
 //   - []byte: The transformed request data in Gemini API format
 func ConvertOpenAIRequestToGemini(modelName string, inputRawJSON []byte, _ bool) []byte {
-	log.Debug("ConvertOpenAIRequestToGemini")
 	rawJSON := bytes.Clone(inputRawJSON)
 	// Base envelope
 	out := []byte(`{"contents":[],"generationConfig":{"thinkingConfig":{"include_thoughts":true}}}`)