feat: add Free subscription tier support (#8864)

## Summary

Add frontend support for a Free subscription tier — login/signup page
restructuring, telemetry instrumentation, and tier-aware billing gating.

## Changes

- **What**: 
- Restructure login/signup pages: OAuth buttons promoted as primary
sign-in method, email login available via progressive disclosure
- Add Free tier badge on Google sign-up button with dynamic credit count
from remote config
- Add `FREE` subscription tier to type system (tier pricing, tier rank,
registry types)
  - Add `isFreeTier` computed to `useSubscription()`
- Disable credit top-up for Free tier users (dialogService,
purchaseCredits, popover CTA)
- Show subscription/upgrade dialog instead of top-up dialog when Free
tier user hits out-of-credits
- Add funnel telemetry: `trackLoginOpened`, enrich `trackSignupOpened`
with `free_tier_badge_shown`, track email toggle clicks

## Review Focus

- Tier gating logic: Free tier users should see "Upgrade" instead of
"Add Credits" and never reach the top-up flow
- Telemetry event design for Mixpanel funnel analysis
- Progressive disclosure UX on login/signup pages

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-8864-feat-add-Free-subscription-tier-support-3076d73d36508133b84ec5f0a67ccb03)
by [Unito](https://www.unito.io)

src/services/dialogService.ts

@@ -17,6 +17,7 @@ import type {
 } from '@/stores/dialogStore'
 
 import type { ComponentAttrs } from 'vue-component-type-helpers'
+import type { SubscriptionDialogReason } from '@/platform/cloud/subscription/composables/useSubscriptionDialog'
 
 // Lazy loaders for dialogs - components are loaded on first use
 const lazyApiNodesSignInContent = () =>
@@ -274,8 +275,15 @@ export const useDialogService = () => {
   async function showTopUpCreditsDialog(options?: {
     isInsufficientCredits?: boolean
   }) {
-    const { isActiveSubscription, type } = useBillingContext()
-    if (!isActiveSubscription.value) return
+    const { isActiveSubscription, isFreeTier, type } = useBillingContext()
+    if (!isActiveSubscription.value || isFreeTier.value) {
+      await showSubscriptionRequiredDialog({
+        reason: options?.isInsufficientCredits
+          ? 'out_of_credits'
+          : 'top_up_blocked'
+      })
+      return
+    }
 
     const component =
       type.value === 'workspace'
@@ -392,7 +400,9 @@ export const useDialogService = () => {
     })
   }
 
-  async function showSubscriptionRequiredDialog() {
+  async function showSubscriptionRequiredDialog(options?: {
+    reason?: SubscriptionDialogReason
+  }) {
     if (!isCloud || !window.__CONFIG__?.subscription_required) {
       return
     }
@@ -400,7 +410,7 @@ export const useDialogService = () => {
     const { useSubscriptionDialog } =
       await import('@/platform/cloud/subscription/composables/useSubscriptionDialog')
     const { show } = useSubscriptionDialog()
-    show()
+    show(options)
   }
 
   // Workspace dialogs - dynamically imported to avoid bundling when feature flag is off