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/platform/telemetry/TelemetryRegistry.ts

@@ -15,6 +15,7 @@ import type {
   PageViewMetadata,
   PageVisibilityMetadata,
   SettingChangedMetadata,
+  SubscriptionMetadata,
   SurveyResponses,
   TabCountMetadata,
   TelemetryDispatcher,
@@ -65,8 +66,11 @@ export class TelemetryRegistry implements TelemetryDispatcher {
     this.dispatch((provider) => provider.trackUserLoggedIn?.())
   }
 
-  trackSubscription(event: 'modal_opened' | 'subscribe_clicked'): void {
-    this.dispatch((provider) => provider.trackSubscription?.(event))
+  trackSubscription(
+    event: 'modal_opened' | 'subscribe_clicked',
+    metadata?: SubscriptionMetadata
+  ): void {
+    this.dispatch((provider) => provider.trackSubscription?.(event, metadata))
   }
 
   trackBeginCheckout(metadata: BeginCheckoutMetadata): void {

src/platform/telemetry/providers/cloud/MixpanelTelemetryProvider.ts

@@ -35,6 +35,7 @@ import type {
   PageVisibilityMetadata,
   RunButtonProperties,
   SettingChangedMetadata,
+  SubscriptionMetadata,
   SurveyResponses,
   TabCountMetadata,
   TelemetryEventName,
@@ -222,13 +223,16 @@ export class MixpanelTelemetryProvider implements TelemetryProvider {
     this.trackEvent(TelemetryEvents.USER_LOGGED_IN)
   }
 
-  trackSubscription(event: 'modal_opened' | 'subscribe_clicked'): void {
+  trackSubscription(
+    event: 'modal_opened' | 'subscribe_clicked',
+    metadata?: SubscriptionMetadata
+  ): void {
     const eventName =
       event === 'modal_opened'
         ? TelemetryEvents.SUBSCRIPTION_REQUIRED_MODAL_OPENED
         : TelemetryEvents.SUBSCRIBE_NOW_BUTTON_CLICKED
 
-    this.trackEvent(eventName)
+    this.trackEvent(eventName, metadata)
   }
 
   trackAddApiCreditButtonClicked(): void {

src/platform/telemetry/types.ts

@@ -12,6 +12,7 @@
  * 3. Check dist/assets/*.js files contain no tracking code
  */
 
+import type { SubscriptionDialogReason } from '@/platform/cloud/subscription/composables/useSubscriptionDialog'
 import type { TierKey } from '@/platform/cloud/subscription/constants/tierPricing'
 import type { BillingCycle } from '@/platform/cloud/subscription/utils/subscriptionTierRank'
 import type { AuditLog } from '@/services/customerEventsService'
@@ -301,6 +302,11 @@ export interface CheckoutAttributionMetadata {
   wbraid?: string
 }
 
+export interface SubscriptionMetadata {
+  current_tier?: string
+  reason?: SubscriptionDialogReason
+}
+
 export interface BeginCheckoutMetadata
   extends Record<string, unknown>, CheckoutAttributionMetadata {
   user_id: string
@@ -321,7 +327,10 @@ export interface TelemetryProvider {
   trackUserLoggedIn?(): void
 
   // Subscription flow events
-  trackSubscription?(event: 'modal_opened' | 'subscribe_clicked'): void
+  trackSubscription?(
+    event: 'modal_opened' | 'subscribe_clicked',
+    metadata?: SubscriptionMetadata
+  ): void
   trackBeginCheckout?(metadata: BeginCheckoutMetadata): void
   trackMonthlySubscriptionSucceeded?(): void
   trackMonthlySubscriptionCancelled?(): void
@@ -512,3 +521,4 @@ export type TelemetryEventProperties =
   | HelpCenterClosedMetadata
   | WorkflowCreatedMetadata
   | EnterLinearMetadata
+  | SubscriptionMetadata