feat: Next generation Stripe billing integration

[niemyjski]

Summary

• Adds new Stripe billing components: ChangePlanDialog and StripeProvider
• Implements Stripe Checkout session creation via API
• Adds billing features to organization API: getBilling, changePlan, getInvoices
• Updates billing pages to use new components
• Updates organization and invoice mappers
• Adds Stripe integration plan document

Changes

• New Svelte components for Stripe integration
• New backend endpoints for billing management
• Updated usage pages to show billing info