feat: integrate Stripe for embedded checkout; update billing API to return client_secret and adjust checkout flow in components

app/welcome/page.tsx

@@ -16,7 +16,6 @@ import {
   type Organization,
   type OrganizationMember,
 } from '@/lib/api/organization'
-import { createCheckoutSession } from '@/lib/api/billing'
 import { createSite, type Site } from '@/lib/api/sites'
 import { setSessionAction } from '@/app/actions/auth'
 import { useAuth } from '@/lib/auth/context'
@@ -218,18 +217,14 @@ function WelcomeContent() {
     try {
       trackWelcomePlanContinue()
       const intent = JSON.parse(raw)
-      const { url } = await createCheckoutSession({
+      const params = new URLSearchParams({
         plan_id: intent.planId,
         interval: intent.interval || 'month',
-        limit: intent.limit ?? 100000,
+        limit: String(intent.limit ?? 100000),
       })
       localStorage.removeItem('pulse_pending_checkout')
-      if (url) {
-        setRedirectingCheckout(true)
-        window.location.href = url
-        return
-      }
-      throw new Error('No checkout URL returned')
+      setRedirectingCheckout(true)
+      router.push(`/checkout?${params.toString()}`)
     } catch (err: unknown) {
       setPlanError(getAuthErrorMessage(err) || (err as Error)?.message || 'Failed to start checkout')
       localStorage.removeItem('pulse_pending_checkout')