refactor(logging): centralize log directory resolution logic

- Introduced `ResolveLogDirectory` function in `logging` package to standardize log directory determination across components.
- Replaced redundant logic in `server`, `global_logger`, and `handlers` with the new utility function.

internal/api/handlers/management/logs.go

@@ -13,7 +13,7 @@ import (
 	"time"
 
 	"github.com/gin-gonic/gin"
-	"github.com/router-for-me/CLIProxyAPI/v6/internal/util"
+	"github.com/router-for-me/CLIProxyAPI/v6/internal/logging"
 )
 
 const (
@@ -360,16 +360,7 @@ func (h *Handler) logDirectory() string {
 	if h.logDir != "" {
 		return h.logDir
 	}
-	if base := util.WritablePath(); base != "" {
-		return filepath.Join(base, "logs")
-	}
-	if h.configFilePath != "" {
-		dir := filepath.Dir(h.configFilePath)
-		if dir != "" && dir != "." {
-			return filepath.Join(dir, "logs")
-		}
-	}
-	return "logs"
+	return logging.ResolveLogDirectory(h.cfg)
 }
 
 func (h *Handler) collectLogFiles(dir string) ([]string, error) {

internal/api/server.go

@@ -261,10 +261,7 @@ func NewServer(cfg *config.Config, authManager *auth.Manager, accessManager *sdk
 	if optionState.localPassword != "" {
 		s.mgmt.SetLocalPassword(optionState.localPassword)
 	}
-	logDir := filepath.Join(s.currentPath, "logs")
-	if base := util.WritablePath(); base != "" {
-		logDir = filepath.Join(base, "logs")
-	}
+	logDir := logging.ResolveLogDirectory(cfg)
 	s.mgmt.SetLogDirectory(logDir)
 	s.localPassword = optionState.localPassword
 

internal/logging/global_logger.go

@@ -121,6 +121,24 @@ func isDirWritable(dir string) bool {
 	return true
 }
 
+// ResolveLogDirectory determines the directory used for application logs.
+func ResolveLogDirectory(cfg *config.Config) string {
+	logDir := "logs"
+	if base := util.WritablePath(); base != "" {
+		return filepath.Join(base, "logs")
+	}
+	if cfg == nil {
+		return logDir
+	}
+	if !isDirWritable(logDir) {
+		authDir := strings.TrimSpace(cfg.AuthDir)
+		if authDir != "" {
+			logDir = filepath.Join(authDir, "logs")
+		}
+	}
+	return logDir
+}
+
 // ConfigureLogOutput switches the global log destination between rotating files and stdout.
 // When logsMaxTotalSizeMB > 0, a background cleaner removes the oldest log files in the logs directory
 // until the total size is within the limit.
@@ -130,12 +148,7 @@ func ConfigureLogOutput(cfg *config.Config) error {
 	writerMu.Lock()
 	defer writerMu.Unlock()
 
-	logDir := "logs"
-	if base := util.WritablePath(); base != "" {
-		logDir = filepath.Join(base, "logs")
-	} else if !isDirWritable(logDir) {
-		logDir = filepath.Join(cfg.AuthDir, "logs")
-	}
+	logDir := ResolveLogDirectory(cfg)
 
 	protectedPath := ""
 	if cfg.LoggingToFile {