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.gen.ts

@@ -0,0 +1,28 @@
+// This file is auto-generated by @hey-api/openapi-ts
+
+import type { ClientOptions } from "./types.gen";
+import {
+  type Config,
+  type ClientOptions as DefaultClientOptions,
+  createClient,
+  createConfig,
+} from "./client";
+
+/**
+ * The `createClientConfig()` function will be called on client initialization
+ * and the returned object will become the client's initial configuration.
+ *
+ * You may want to initialize your client this way instead of calling
+ * `setConfig()`. This is useful for example if you're using Next.js
+ * to ensure your client always has the correct values.
+ */
+export type CreateClientConfig<T extends DefaultClientOptions = ClientOptions> =
+  (
+    override?: Config<DefaultClientOptions & T>,
+  ) => Config<Required<DefaultClientOptions> & T>;
+
+export const client = createClient(
+  createConfig<ClientOptions>({
+    baseUrl: "http://127.0.0.1:1250",
+  }),
+);