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/claude/init.go

@@ -8,8 +8,8 @@ import (
 
 func init() {
 	translator.Register(
-		CLAUDE,
-		GEMINI,
+		Claude,
+		Gemini,
 		ConvertClaudeRequestToGemini,
 		interfaces.TranslateResponse{
 			Stream:    ConvertGeminiResponseToClaude,

internal/translator/gemini/gemini-cli/init.go

@@ -8,8 +8,8 @@ import (
 
 func init() {
 	translator.Register(
-		GEMINICLI,
-		GEMINI,
+		GeminiCLI,
+		Gemini,
 		ConvertGeminiCLIRequestToGemini,
 		interfaces.TranslateResponse{
 			Stream:    ConvertGeminiResponseToGeminiCLI,

internal/translator/gemini/gemini/init.go

@@ -10,8 +10,8 @@ import (
 // The request converter ensures missing or invalid roles are normalized to valid values.
 func init() {
 	translator.Register(
-		GEMINI,
-		GEMINI,
+		Gemini,
+		Gemini,
 		ConvertGeminiRequestToGemini,
 		interfaces.TranslateResponse{
 			Stream:    PassthroughGeminiResponseStream,

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,

internal/translator/gemini/openai/responses/init.go

@@ -8,8 +8,8 @@ import (
 
 func init() {
 	translator.Register(
-		OPENAI_RESPONSE,
-		GEMINI,
+		OpenaiResponse,
+		Gemini,
 		ConvertOpenAIResponsesRequestToGemini,
 		interfaces.TranslateResponse{
 			Stream:    ConvertGeminiResponseToOpenAIResponses,