llm integration

## LLM Integration

AI-powered Postgres assistant integrated into the workbench.

### Goals

- **SQL writing assistance** — help compose queries, explain syntax, suggest schema designs
- **Query analysis & optimization** — analyze EXPLAIN plans, suggest indexes, rewrite slow queries (ties into existing pev2 visualization)
- **Schema review & best practices** — naming issues, normalization suggestions, anti-pattern detection
- **Conversational DB exploration** — natural language to SQL, ask questions about your data

### Architecture

**BYOK (Bring Your Own Key)** — users configure their own LLM provider + API key. Server proxies requests (solves CORS), never persists keys.

**Premium tier** — GitHub sponsors could get access to a hosted model (inference cost offset by sponsorship).

#### Existing Infrastructure

Server-side multi-provider abstraction already built at `server/ai/`:

- `@effect/ai` with four providers: OpenAI, Anthropic, Google, OpenRouter
- Model registry with auto-detection (`resolveProvider("gpt-4o")` → `"openai"`)
- `generateText()` with BYOK via `Redacted` API keys
- `generateTextFromEnv()` for server-configured keys (premium tier)

Client-side VS Code Chat service already registered (`getChatServiceOverride()`).

#### What's Needed

1. **Server: streaming chat route** — `POST /api/ai/chat` using `AiLanguageModel.streamText()` from `@effect/ai`, returns SSE stream. Client sends API key per-request in a header.

2. **Client: `LanguageModelChatProvider`** — registers with `vscode.lm.registerLanguageModelChatProvider()`, proxies to server streaming endpoint. Makes the multi-provider backend available to any VS Code chat feature.

3. **Client: `@pg` ChatParticipant** — registered via `vscode.chat.createChatParticipant()` with commands:
- `/explain` — explain current query or EXPLAIN plan
- `/optimize` — suggest improvements for a query
- `/schema` — review current schema for anti-patterns
- `/ask` — natural language to SQL
- Assembles on-demand context from existing introspection data (tables, columns, types, indexes) and current editor content.

4. **Client: API key settings UI** — new section in Account Settings (or dedicated panel) for provider + API key configuration. Stored in `vscode.SecretStorage`.

### UX Surfaces

- **Chat sidebar** — VS Code Chat panel (`@pg` participant) for open-ended questions
- **Inline notebook cells** — natural language cells in SQL notebooks → generated SQL in next cell
- Both entry points share the same backend

### References

- VS Code Chat API: [chat-sample](https://github.com/microsoft/vscode-extension-samples/tree/main/chat-sample)
- VS Code inline completions: [inline-completions](https://github.com/microsoft/vscode-extension-samples/tree/main/inline-completions)
- VS Code diffs: [QuickDiffProvider](https://code.visualstudio.com/api/references/vscode-api#QuickDiffProvider), [source-control-sample](https://github.com/microsoft/vscode-extension-samples/blob/main/source-control-sample/src/fiddleRepository.ts)
- [postgresai](https://github.com/postgres-ai/postgresai) — Apache 2.0 Postgres observability with AI-ready structured output (health checks less relevant for in-memory PGlite, but domain knowledge is useful)
- Postgres RAG: [part 1](http://bonesmoses.org/2024/pg-phriday-dirty-postgres-rag/), [part 2](http://bonesmoses.org/2024/pg-phriday-brand-new-rag/)
- [premsql](https://github.com/premAI-io/premsql)

Start by reading the existing server/ai/ abstraction and the registered getChatServiceOverride() client service. Map the requested POST /api/ai/chat SSE route, LanguageModelChatProvider, @pg participant commands, and SecretStorage settings UI to existing client and server entry points. Done means the listed chat surfaces can use BYOK providers through the shared streaming backend.

Written by the indexing model from the issue text.