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/api/handlers/claude/code_handlers.go

@@ -43,7 +43,7 @@ func NewClaudeCodeAPIHandler(apiHandlers *handlers.BaseAPIHandler) *ClaudeCodeAP
 
 // HandlerType returns the identifier for this handler implementation.
 func (h *ClaudeCodeAPIHandler) HandlerType() string {
-	return CLAUDE
+	return Claude
 }
 
 // Models returns a list of models supported by this handler.

internal/api/handlers/gemini/gemini-cli_handlers.go

@@ -38,7 +38,7 @@ func NewGeminiCLIAPIHandler(apiHandlers *handlers.BaseAPIHandler) *GeminiCLIAPIH
 
 // HandlerType returns the type of this handler.
 func (h *GeminiCLIAPIHandler) HandlerType() string {
-	return GEMINICLI
+	return GeminiCLI
 }
 
 // Models returns a list of models supported by this handler.

internal/api/handlers/gemini/gemini_handlers.go

@@ -38,7 +38,7 @@ func NewGeminiAPIHandler(apiHandlers *handlers.BaseAPIHandler) *GeminiAPIHandler
 
 // HandlerType returns the identifier for this handler implementation.
 func (h *GeminiAPIHandler) HandlerType() string {
-	return GEMINI
+	return Gemini
 }
 
 // Models returns the Gemini-compatible model metadata supported by this handler.

internal/api/handlers/management/auth_files.go

@@ -147,7 +147,7 @@ func (h *Handler) UploadAuthFile(c *gin.Context) {
 		c.JSON(500, gin.H{"error": fmt.Sprintf("failed to write file: %v", errWrite)})
 		return
 	}
-	if err := h.registerAuthFromFile(ctx, dst, data); err != nil {
+	if err = h.registerAuthFromFile(ctx, dst, data); err != nil {
 		c.JSON(500, gin.H{"error": err.Error()})
 		return
 	}

internal/api/handlers/openai/openai_handlers.go

@@ -44,7 +44,7 @@ func NewOpenAIAPIHandler(apiHandlers *handlers.BaseAPIHandler) *OpenAIAPIHandler
 
 // HandlerType returns the identifier for this handler implementation.
 func (h *OpenAIAPIHandler) HandlerType() string {
-	return OPENAI
+	return OpenAI
 }
 
 // Models returns the OpenAI-compatible model metadata supported by this handler.

internal/api/handlers/openai/openai_responses_handlers.go

@@ -43,7 +43,7 @@ func NewOpenAIResponsesAPIHandler(apiHandlers *handlers.BaseAPIHandler) *OpenAIR
 
 // HandlerType returns the identifier for this handler implementation.
 func (h *OpenAIResponsesAPIHandler) HandlerType() string {
-	return OPENAI_RESPONSE
+	return OpenaiResponse
 }
 
 // Models returns the OpenAIResponses-compatible model metadata supported by this handler.
@@ -161,6 +161,7 @@ func (h *OpenAIResponsesAPIHandler) forwardResponsesStream(c *gin.Context, flush
 			return
 		case chunk, ok := <-data:
 			if !ok {
+				_, _ = c.Writer.Write([]byte("\n"))
 				flusher.Flush()
 				cancel(nil)
 				return

internal/api/server.go

@@ -439,38 +439,14 @@ func (s *Server) UpdateClients(cfg *config.Config) {
 		s.mgmt.SetAuthManager(s.handlers.AuthManager)
 	}
 
-	// Count types from AuthManager state + config
-	authFiles := 0
-	glAPIKeyCount := 0
-	claudeAPIKeyCount := 0
-	codexAPIKeyCount := 0
+	// Count client sources from configuration and auth directory
+	authFiles := util.CountAuthFiles(cfg.AuthDir)
+	glAPIKeyCount := len(cfg.GlAPIKey)
+	claudeAPIKeyCount := len(cfg.ClaudeKey)
+	codexAPIKeyCount := len(cfg.CodexKey)
 	openAICompatCount := 0
-
-	if s.handlers != nil && s.handlers.AuthManager != nil {
-		for _, a := range s.handlers.AuthManager.List() {
-			if a == nil {
-				continue
-			}
-			if a.Attributes != nil {
-				if p := a.Attributes["path"]; p != "" {
-					authFiles++
-					continue
-				}
-			}
-			switch strings.ToLower(a.Provider) {
-			case "gemini":
-				glAPIKeyCount++
-			case "claude":
-				claudeAPIKeyCount++
-			case "codex":
-				codexAPIKeyCount++
-			}
-		}
-	}
-	if cfg != nil {
-		for i := range cfg.OpenAICompatibility {
-			openAICompatCount += len(cfg.OpenAICompatibility[i].APIKeys)
-		}
+	for i := range cfg.OpenAICompatibility {
+		openAICompatCount += len(cfg.OpenAICompatibility[i].APIKeys)
 	}
 
 	total := authFiles + glAPIKeyCount + claudeAPIKeyCount + codexAPIKeyCount + openAICompatCount