feat: implement cross-tab coordination for token refresh and enhance logout handling

frontend/vue-app/src/stores/auth.ts

@@ -22,6 +22,7 @@ if (hasLocalStorage) {
         parentAuthExpiresAt.value = parsed.expiresAt
         isParentPersistent.value = true
         isParentAuthenticated.value = true
+        startParentExpiryWatcher()
       } else {
         localStorage.removeItem(PARENT_AUTH_KEY)
       }
@@ -81,6 +82,9 @@ export function authenticateParent(persistent: boolean) {
 }
 
 export function logoutParent() {
+  if (hasLocalStorage && typeof localStorage.removeItem === 'function') {
+    localStorage.removeItem(PARENT_AUTH_KEY)
+  }
   applyParentLoggedOutState()
   broadcastParentLogoutEvent()
 }
@@ -89,9 +93,6 @@ function applyParentLoggedOutState() {
   parentAuthExpiresAt.value = null
   isParentPersistent.value = false
   isParentAuthenticated.value = false
-  if (hasLocalStorage && typeof localStorage.removeItem === 'function') {
-    localStorage.removeItem(PARENT_AUTH_KEY)
-  }
   stopParentExpiryWatcher()
 }
 
@@ -105,7 +106,11 @@ function broadcastParentLogoutEvent() {
 
 export function loginUser() {
   isUserLoggedIn.value = true
-  // Always start in child mode after login
+  // Always start in child mode after login. Also explicitly remove persistent parent
+  // auth from localStorage so a fresh login always starts in child mode.
+  if (hasLocalStorage && typeof localStorage.removeItem === 'function') {
+    localStorage.removeItem(PARENT_AUTH_KEY)
+  }
   applyParentLoggedOutState()
 }