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/core/auth.ts

@@ -0,0 +1,40 @@
+export type AuthToken = string | undefined;
+
+export interface Auth {
+  /**
+   * Which part of the request do we use to send the auth?
+   *
+   * @default 'header'
+   */
+  in?: "header" | "query" | "cookie";
+  /**
+   * Header or query parameter name.
+   *
+   * @default 'Authorization'
+   */
+  name?: string;
+  scheme?: "basic" | "bearer";
+  type: "apiKey" | "http";
+}
+
+export const getAuthToken = async (
+  auth: Auth,
+  callback: ((auth: Auth) => Promise<AuthToken> | AuthToken) | AuthToken,
+): Promise<string | undefined> => {
+  const token =
+    typeof callback === "function" ? await callback(auth) : callback;
+
+  if (!token) {
+    return;
+  }
+
+  if (auth.scheme === "bearer") {
+    return `Bearer ${token}`;
+  }
+
+  if (auth.scheme === "basic") {
+    return `Basic ${btoa(token)}`;
+  }
+
+  return token;
+};