refactor(utils): extract formatRelativeTime to utils/time.ts

- create utils/time.ts for centralized time formatting

- remove duplicate from auth/commands/types.ts

- re-export for backward compatibility

- export from utils/index.ts

src/auth/commands/types.ts

@@ -7,6 +7,9 @@
 import ProfileRegistry from '../profile-registry';
 import { InstanceManager } from '../../management/instance-manager';
 
+// Re-export for backward compatibility
+export { formatRelativeTime } from '../../utils/time';
+
 /**
  * Command arguments parsed from CLI
  */
@@ -61,20 +64,3 @@ export function parseArgs(args: string[]): AuthCommandArgs {
     yes: args.includes('--yes') || args.includes('-y'),
   };
 }
-
-/**
- * Format relative time (e.g., "2h ago", "1d ago")
- */
-export function formatRelativeTime(date: Date): string {
-  const now = Date.now();
-  const diff = now - date.getTime();
-
-  const minutes = Math.floor(diff / 60000);
-  const hours = Math.floor(diff / 3600000);
-  const days = Math.floor(diff / 86400000);
-
-  if (days > 0) return `${days}d ago`;
-  if (hours > 0) return `${hours}h ago`;
-  if (minutes > 0) return `${minutes}m ago`;
-  return 'just now';
-}

src/utils/index.ts

@@ -6,6 +6,9 @@
 // UI utilities (main export)
 export * from './ui';
 
+// Time utilities
+export * from './time';
+
 // Shell execution
 export { execClaude, escapeShellArg } from './shell-executor';
 

src/utils/time.ts

@@ -0,0 +1,22 @@
+/**
+ * Time Formatting Utilities
+ *
+ * Centralized date/time formatting functions.
+ */
+
+/**
+ * Format relative time (e.g., "2h ago", "1d ago")
+ */
+export function formatRelativeTime(date: Date): string {
+  const now = Date.now();
+  const diff = now - date.getTime();
+
+  const minutes = Math.floor(diff / 60000);
+  const hours = Math.floor(diff / 3600000);
+  const days = Math.floor(diff / 86400000);
+
+  if (days > 0) return `${days}d ago`;
+  if (hours > 0) return `${hours}h ago`;
+  if (minutes > 0) return `${minutes}m ago`;
+  return 'just now';
+}