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/(app)/rooms/useRoomList.tsx

@@ -1,10 +1,10 @@
 import { useEffect, useState } from "react";
 import { useError } from "../../(errors)/errorContext";
 import useApi from "../../lib/useApi";
-import { Page_Room_ } from "../../api";
+import { PageRoom } from "../../api";
 
 type RoomList = {
-  response: Page_Room_ | null;
+  response: PageRoom | null;
   loading: boolean;
   error: Error | null;
   refetch: () => void;
@@ -12,7 +12,7 @@ type RoomList = {
 
 //always protected
 const useRoomList = (page: number): RoomList => {
-  const [response, setResponse] = useState<Page_Room_ | null>(null);
+  const [response, setResponse] = useState<PageRoom | null>(null);
   const [loading, setLoading] = useState<boolean>(true);
   const [error, setErrorState] = useState<Error | null>(null);
   const { setError } = useError();