Add SQL-backed Effect chat persistence wiring

[lloydrichards]

Parent

Part of #139.

What to build

Add an optional chat persistence module that wires Effect Chat.Persistence to the SQL persistence layer provided by db-sqlite.

This module should provide minimal boilerplate for persisted Effect chat history. It should not introduce app-specific chat metadata, chat list/get/delete APIs, titles, models, users, threads, or durable active-run metadata.

Helpful context

• SQLite foundation: Add reusable db-sqlite foundation module #146
• Effect Chat persistence: .reference/effect/packages/effect/src/unstable/ai/Chat.ts
• Effect Persistence SQL layers: .reference/effect/packages/effect/src/unstable/persistence/Persistence.ts
• Current chat runtime: packages/catalog/src/registry/content/chat.ts

Acceptance criteria

• Add an optional chat persistence module that depends on db-sqlite.
• Provide Effect Persistence.layerSql or the appropriate SQL-backed Effect Persistence layer using the generated SQLite foundation.
• Provide Chat.layerPersisted({ storeId: "chat" }) or equivalent generated layer wiring.
• Keep chat_ask and chat-react-client unchanged.
• Do not add chat metadata tables, chat list/get/delete APIs, titles, models, users, threads, or durable active-run metadata.
• Document where a future stable chat/thread persistence key would plug into ChatRuntime or a future RPC.
• Add tests or generated-workspace validation proving the persistence layer composes with the generated server runtime.

Blocked by

• Add reusable db-sqlite foundation module #146