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/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 {