refactor: standardize constant naming and improve file-based auth handling

- Renamed constants from uppercase to CamelCase for consistency.
- Replaced redundant file-based auth handling logic with the new `util.CountAuthFiles` helper.
- Fixed various error-handling inconsistencies and enhanced robustness in file operations.
- Streamlined auth client reload logic in server and watcher components.
- Applied minor code readability improvements across multiple packages.

internal/translator/gemini/openai/chat-completions/init.go

@@ -8,8 +8,8 @@ import (
 
 func init() {
 	translator.Register(
-		OPENAI,
-		GEMINI,
+		OpenAI,
+		Gemini,
 		ConvertOpenAIRequestToGemini,
 		interfaces.TranslateResponse{
 			Stream:    ConvertGeminiResponseToOpenAI,