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-cli/gemini_gemini-cli_request.go

@@ -17,7 +17,6 @@ import (
 // It extracts the model name, system instruction, message contents, and tool declarations
 // from the raw JSON request and returns them in the format expected by the internal client.
 func ConvertGeminiCLIRequestToGemini(_ string, inputRawJSON []byte, _ bool) []byte {
-	log.Debug("ConvertGeminiCLIRequestToGemini")
 	rawJSON := bytes.Clone(inputRawJSON)
 	modelResult := gjson.GetBytes(rawJSON, "model")
 	rawJSON = []byte(gjson.GetBytes(rawJSON, "request").Raw)