Add owner profile-mode analytics funnel

[sarthakagrawal927]

Closes #45

Summary

• add typed owner-only PostHog events for successful profile-mode configuration and generation
• make chat, encyclopedia, newspaper, and roast configuration comparable without public visitor tracking
• normalize generated-mode captures under the fixed Karte project and source taxonomy
• document the privacy boundary and archive the OpenSpec change

Validation

• pnpm lint
• pnpm typecheck
• pnpm test (83 tests)
• pnpm build
• pnpm docs:check (0 errors; 8 pre-existing archive warnings)
• OpenSpec strict validation (4/4)