feat: add email verification check for cloud onboarding (#5636)

## Summary
- Added email verification flow for new users during onboarding
- Implemented invite code claiming with proper validation 
- Updated API endpoints from `/invite/` to `/invite_code/` for
consistency

## Changes

### Email Verification
- Added `CloudVerifyEmailView` component with email verification UI
- Added email verification check after login in `CloudLoginView`
- Added `isEmailVerified` property to Firebase auth store
- Users must verify email before claiming invite codes

### Invite Code Flow
- Enhanced `CloudClaimInviteView` with full claim invite functionality
- Updated `InviteCheckView` to route users based on email verification
status
- Modified API to return both `claimed` and `expired` status for invite
codes
- Added proper error handling and Sentry logging for invite operations

### API Updates
- Changed endpoint paths from `/invite/` to `/invite_code/` 
- Updated `getInviteCodeStatus()` to return `{ claimed: boolean;
expired: boolean }`
- Updated `claimInvite()` to return `{ success: boolean; message: string
}`

### UI/UX Improvements
- Added Korean translations for all new strings
- Improved button styling and layout in survey and waitlist views
- Added proper loading states and error handling

## Test Plan
- [ ] Test new user signup flow with email verification
- [ ] Test invite code validation (expired/claimed/valid codes)
- [ ] Test email verification redirect flow
- [ ] Test invite claiming after email verification
- [ ] Verify Korean translations display correctly

🤖 Generated with [Claude Code](https://claude.ai/code)

---------

Co-authored-by: Claude <noreply@anthropic.com>

src/platform/onboarding/cloud/CloudVerifyEmailView.vue

@@ -1,20 +1,108 @@
 <template>
-  <div>
-    <h1>{{ t('cloudVerifyEmail_title') }}</h1>
+  <div class="px-6 py-8 max-w-[640px] mx-auto">
+    <!-- Back button -->
+    <button
+      type="button"
+      class="flex items-center justify-center size-10 rounded-lg bg-transparent border border-white text-foreground/80"
+      aria-label="{{ t('cloudVerifyEmail_back') }}"
+      @click="goBack"
+    >
+      <i class="pi pi-arrow-left" />
+    </button>
+
+    <!-- Title -->
+    <h1 class="mt-8 text-2xl font-semibold">
+      {{ t('cloudVerifyEmail_title') }}
+    </h1>
+
+    <!-- Body copy -->
+    <p class="mt-6 text-base text-foreground/80">
+      {{ t('cloudVerifyEmail_sent') }}
+    </p>
+    <p class="mt-3 text-base font-medium">{{ authStore.userEmail }}</p>
+
+    <p class="mt-6 text-base text-foreground/80">
+      {{ t('cloudVerifyEmail_clickToContinue') }}
+    </p>
+
+    <p class="mt-10 text-base text-foreground/80">
+      {{ t('cloudVerifyEmail_didntReceive') }}
+      <span class="text-blue-400 no-underline cursor-pointer" @click="onSend">
+        {{ t('cloudVerifyEmail_resend') }}</span
+      >
+    </p>
   </div>
 </template>
 
 <script setup lang="ts">
 import { onMounted } from 'vue'
 import { useI18n } from 'vue-i18n'
+import { useRoute, useRouter } from 'vue-router'
 
-// import { verifyEmail } from '@/api/auth'
-import router from '@/router'
+import { useFirebaseAuthStore } from '@/stores/firebaseAuthStore'
+import { useToastStore } from '@/stores/toastStore'
 
+const authStore = useFirebaseAuthStore()
+
+const router = useRouter()
+const route = useRoute()
 const { t } = useI18n()
 
+const goBack = async () => {
+  const inviteCode = route.query.inviteCode as string | undefined
+  const authStore = useFirebaseAuthStore()
+  // If the user is already verified (email link already clicked),
+  // continue to the next step automatically.
+  if (authStore.isEmailVerified) {
+    await router.push({
+      name: 'cloud-invite-check',
+      query: inviteCode ? { inviteCode } : {}
+    })
+  } else {
+    await router.push({
+      name: 'cloud-login',
+      query: {
+        inviteCode
+      }
+    })
+  }
+}
+
+async function onSend() {
+  try {
+    await authStore.verifyEmail()
+    useToastStore().add({
+      severity: 'success',
+      summary: t('cloudVerifyEmail_toast_success', {
+        email: authStore.userEmail
+      })
+    })
+  } catch (e) {
+    useToastStore().add({
+      severity: 'error',
+      summary: t('cloudVerifyEmail_toast_failed')
+    })
+  }
+}
+
 onMounted(async () => {
-  // verifyEmail()
-  await router.push({ name: 'cloud-invite-check' })
+  // When this screen loads via invite flow,
+  // ensure the invite code stays in the URL for the next step.
+  const inviteCode = route.query.inviteCode as string | undefined
+
+  // If the user is already verified (email link already clicked),
+  // continue to the next step automatically.
+  if (authStore.isEmailVerified) {
+    if (inviteCode) {
+      await router.push({
+        name: 'cloud-invite-check',
+        query: inviteCode ? { inviteCode } : {}
+      })
+    } else {
+      await router.push({ name: 'cloud-user-check' })
+    }
+  } else {
+    await onSend()
+  }
 })
 </script>