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/composables/billing/types.ts

@@ -70,6 +70,11 @@ export interface BillingState {
    * Equivalent to `subscription.value?.isActive ?? false`
    */
   isActiveSubscription: ComputedRef<boolean>
+  /**
+   * Whether the current billing context has a FREE tier subscription.
+   * Workspace-aware: reflects the active workspace's tier, not the user's personal tier.
+   */
+  isFreeTier: ComputedRef<boolean>
 }
 
 export interface BillingContext extends BillingState, BillingActions {

src/composables/billing/useBillingContext.ts

@@ -120,6 +120,8 @@ function useBillingContextInternal(): BillingContext {
     toValue(activeContext.value.isActiveSubscription)
   )
 
+  const isFreeTier = computed(() => subscription.value?.tier === 'FREE')
+
   function getMaxSeats(tierKey: TierKey): number {
     if (type.value === 'legacy') return 1
 
@@ -238,6 +240,7 @@ function useBillingContextInternal(): BillingContext {
     isLoading,
     error,
     isActiveSubscription,
+    isFreeTier,
     getMaxSeats,
 
     initialize,

src/composables/billing/useLegacyBilling.ts

@@ -40,6 +40,7 @@ export function useLegacyBilling(): BillingState & BillingActions {
   const error = ref<string | null>(null)
 
   const isActiveSubscription = computed(() => legacyIsActiveSubscription.value)
+  const isFreeTier = computed(() => subscriptionTier.value === 'FREE')
 
   const subscription = computed<SubscriptionInfo | null>(() => {
     if (!legacyIsActiveSubscription.value && !subscriptionTier.value) {
@@ -85,6 +86,10 @@ export function useLegacyBilling(): BillingState & BillingActions {
     error.value = null
     try {
       await Promise.all([fetchStatus(), fetchBalance()])
+      // Re-fetch balance if free tier credits were just lazily granted
+      if (isFreeTier.value && balance.value?.amountMicros === 0) {
+        await fetchBalance()
+      }
       isInitialized.value = true
     } catch (err) {
       error.value =
@@ -173,6 +178,7 @@ export function useLegacyBilling(): BillingState & BillingActions {
     isLoading,
     error,
     isActiveSubscription,
+    isFreeTier,
 
     // Actions
     initialize,