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/cloud/subscription/utils/subscriptionTierRank.ts

@@ -2,7 +2,7 @@ import type { TierKey } from '@/platform/cloud/subscription/constants/tierPricin
 
 export type BillingCycle = 'monthly' | 'yearly'
 
-type RankedTierKey = Exclude<TierKey, 'founder'>
+type RankedTierKey = Exclude<TierKey, 'founder' | 'free'>
 type RankedPlanKey = `${BillingCycle}-${RankedTierKey}`
 
 interface PlanDescriptor {
@@ -28,7 +28,7 @@ const toRankedPlanKey = (
   tierKey: TierKey,
   billingCycle: BillingCycle
 ): RankedPlanKey | null => {
-  if (tierKey === 'founder') return null
+  if (tierKey === 'founder' || tierKey === 'free') return null
   return `${billingCycle}-${tierKey}` as RankedPlanKey
 }
 

src/platform/cloud/subscription/utils/tierBenefits.ts

@@ -0,0 +1,67 @@
+import {
+  getTierCredits,
+  getTierFeatures
+} from '@/platform/cloud/subscription/constants/tierPricing'
+import type { TierKey } from '@/platform/cloud/subscription/constants/tierPricing'
+
+type BenefitType = 'metric' | 'feature' | 'icon'
+
+export interface TierBenefit {
+  key: string
+  type: BenefitType
+  label: string
+  value?: string
+  icon?: string
+}
+
+export function getCommonTierBenefits(
+  key: TierKey,
+  t: (key: string, params?: Record<string, unknown>) => string,
+  n: (value: number) => string
+): TierBenefit[] {
+  const benefits: TierBenefit[] = []
+  const isFree = key === 'free'
+
+  if (isFree) {
+    const credits = getTierCredits(key)
+    if (credits !== null) {
+      benefits.push({
+        key: 'monthlyCredits',
+        type: 'metric',
+        value: n(credits),
+        label: t('subscription.monthlyCreditsLabel')
+      })
+    }
+  }
+
+  benefits.push({
+    key: 'maxDuration',
+    type: 'metric',
+    value: t(`subscription.maxDuration.${key}`),
+    label: t('subscription.maxDurationLabel')
+  })
+
+  benefits.push({
+    key: 'gpu',
+    type: 'feature',
+    label: t('subscription.gpuLabel')
+  })
+
+  if (!isFree) {
+    benefits.push({
+      key: 'addCredits',
+      type: 'feature',
+      label: t('subscription.addCreditsLabel')
+    })
+  }
+
+  if (getTierFeatures(key).customLoRAs) {
+    benefits.push({
+      key: 'customLoRAs',
+      type: 'feature',
+      label: t('subscription.customLoRAsLabel')
+    })
+  }
+
+  return benefits
+}