feat: add background information field to room model

- Add background_information field to Room database table and model
- Create database migration for the new field
- Update API schemas (CreateRoom, UpdateRoom) to handle background_information
- Integrate room context into AI summarization prompts
- Add background_information field to frontend room form
- Update TypeScript types from regenerated OpenAPI spec

The background information will be used to provide context for AI-generated
summaries, helping create more appropriate and relevant meeting summaries.

🤖 Generated with [opencode](https://opencode.ai)

Co-Authored-By: opencode <noreply@opencode.ai>

www/app/api/client/index.ts

@@ -0,0 +1,22 @@
+export type { Auth } from "../core/auth";
+export type { QuerySerializerOptions } from "../core/bodySerializer";
+export {
+  formDataBodySerializer,
+  jsonBodySerializer,
+  urlSearchParamsBodySerializer,
+} from "../core/bodySerializer";
+export { buildClientParams } from "../core/params";
+export { createClient } from "./client";
+export type {
+  Client,
+  ClientOptions,
+  Config,
+  CreateClientConfig,
+  Options,
+  OptionsLegacyParser,
+  RequestOptions,
+  RequestResult,
+  ResponseStyle,
+  TDataShape,
+} from "./types";
+export { createConfig, mergeHeaders } from "./utils";