Drizzle Chat Persistence

The deliverable is one file in the app — src/lib/chat-persistence.ts — exporting a ChatPersistence built from the app's existing Drizzle db. Plus four tables added to the app's existing schema file and a migration generated through the app's existing drizzle-kit setup.

Do not create a package, a second db instance, a migration runner, or a drizzle.config.ts. The app has those.

Read the Store Reference (docs/persistence/store-reference.md) for the store contracts and invariants, and ai-persistence/stores for the shape rules. Every store below mirrors the reference in-memory backend in @tanstack/ai-persistence (memory.ts); the shared conformance testkit is the proof.

1. Read the app before writing anything